Thanks so much in advance!
You are doing the right thing, you CAN do this.
Mine was starving and dehydrated, but she made it... she wasn't as little as your kitten though!
Here is some advice I found online just now, it looks really sound:
Nutrition in the first several days is critical to the survival of a newborn kitten. Follow these step-by-step instructions for bottle-feeding a newborn kitten, including precautions to take, helpful tips, and the follow-through "cleanup job," including stimulation of the bowels and urinary tract, and you will be a competent surrogate cat mother in no time.
Time Required: 10 to 20 minutes several times a day
Prepare your supplies. Sterilize the kitten-sized baby bottles and nipples in a boiling water bath for about 5 minutes. Cool before using. Place a large towel, a rough-textured washcloth and a bowl of warm water on a table next to a comfortable chair.
Fill bottle with desired amount (see tips) of commercial kitten milk replacement such as KMR, or an emergency formula if you can't get to a pet food store right away. Warm the formula by placing the bottle in a bowl of very hot water, then test it against your forearm. It should be 95° to 100° fahrenheit, or approximately body temperature. Test the nipple to ensure the flow is just right.
Sit in the chair with the towel folded in your lap. Place the kitten prone (face down) on your lap. Make sure the kitten is warm before feeding. Feeding formula to a cold kitten can cause serious digestive problems. Without raising the kitten's head, place the nipple in his mouth. He should start nursing right away. If all goes well, let him continue nursing until finished. Do not overfeed.
If the kitten does not start nursing right away, or if he seems to have trouble getting the milk, check the nipple again. It should not drip milk when held upside down, but should drip given a small amount of pressure. It may also be helpful to stroke his head or gently pet his back to start his nursing reflexes, but once he gets the idea, he will nurse readily.
Much like human babies, kittens may need "burping" after nursing. This is best accomplished by holding one hand under his abdomen and gently patting his upper back. Not too hard - you don't want him to vomit. If he doesn't burp right away, go to step #6.
The mother cat will stimulate her kitten's elimination by licking his anus and genital area with her rough tongue. You can emulate this process with a warm, damp, rough washcloth or dampened paper towel. It may take a couple of feedings to see results, so don't despair if he doesn't defecate right away. Urinating may take a bit longer.
Your kitten will want to sleep after nursing, so put him back into his bed to let him sleep undisturbed.
Your newborn kitten will need approximately 32 cc (1.1 oz.) of formula a day, divided into 9 - 12 feedings a day, depending on his size and condition. Count on feeding him every two hours or so, around the clock, for starters. Yes, it's a demanding job, but intensely rewarding to watch your newborn develop and grow.
In a pinch, if you can't get kitten baby bottles, an eye dropper will do. Be very careful to drop only a very small amount on the kitten's tongue to avoid aspiration of the formula into his lungs.
Weigh your kitten every day, on a food scale covered with a clean cloth. He should gain 1/2 oz. ever day for about the first two weeks.
Buy several bottles and nipples, then sterilize and fill a number of them at once, and refrigerate. Warm as needed, following the directions above.
Proper positioning of the kitten is critical. Raising his head may cause aspiration of the formula into the kitten's lungs, which could be fatal.
What You Need:
Commercial Milk Replacer
Nursing Bottles & Nipples
Coarse wash rag
You need the kitten formula. Whole milk is not an adequate substitute for mother cat's milk (just like it's not a substitute for human milk).
The Pet Ag nipples are the best. Others are OK, but not as good. And usually, the nipple the kitten eats from first is the kind they will prefer.
I've bottle fed many kittens, and yes, he will need to be fed every few hours - all day, all night.
I ended up emptying out a plastic "bills" box to carry one kitten to work. It had a slot through which you are supposed to slip the bills, and a large interior space for files, etc. I just took out all the innards, lined it with towels and took the kitten to work with me. Nobody (but my immediate area co-workers) knew anything was up.
Kittens, like infant humans, really want and need contact with another living thing. Do you have a sling? I've raised several "sling kitties", and they LOVE it.
For the kitten that I took to work with me, I wore pants, and tucked my shirt into the pants. Then I slipped the kitten inside my shirt (down near my waist) and tucked that little corner of the shirt back in. This helped the kitten regulate it's own body temperature, helped keep it warm in the overly air conditioned office. After a week of this, kitten's eyes were open, and it started crawling around and around my waist - SO FUNNY.
Good luck. Definitely go over to the Orphan Kittens group - they can give you LOTS of support.
Ann-Marita. I deleted my usual signature due to, oh, wait, if I say why, that might give too much away.
In breeding situations, if there are two moms with kittens they often swap kittens. One will take an extra one, that sort of thing. : They tend to be pretty receptive to it LOL. I had two litters with two different queens when I was helping out a breeder friend and they did just that!
So, I'd contact some vets/rescue organizations first and try to find a queen who has recently birthed who could nurse/care for her. If it is truly a "newborn" kitten as you've said it's likely the kitten will die otherwise.
Perpetually breastfeeding or pregnant ENFP mom to a lot of kids...wife to a midwestern nice guy...living in tropical paradise...pink cats and homebirths rock!
Definitely you need to feed frequently, and keep him/her warm. We used a ceramic heating element over her box at night, and in the day my teenager held her a lot.
I also second Christy, start calling rescues and vet's offices to find a mom cat with babies about as old as your guy. You can bottle raise a kitten, but it's HARD. lots of work and if you can find a willing mom cat, so much the better.
The other thing to remember is to keep the kitten warm! warm kitten eat and kittens who eat have a better chance of living.
Once my two year old daughter realized she wasn't going to be able to play with the kitten she was NOT happy with the situation--she's an only and has never had to really share my attention before. That was a real eye opener.
My husband got home from work and was able to feed it from the bottle, he grew up bottle feeding abandoned pets so he had a a clue whereas I had NO idea...Anyway, he fed it twice before about 10 p.m. and then we put it to bed in a box in a warm room with a hot water bottle and the baby monitor. I didn't hear a peep all night and was concerned that maybe she passed but when I checked in at 6 she was sleeping soundly and had no interest in waking up. I'm guessing it was probably the first full-tummied/cozy warm night of her life. She woke up at about 7:30 and my husband fed her again and tried to help her pee.
We called our friend at animal services and they do have a litter of newborns there that they're going and try to set her up with. If she's not accepted then my friend is going to take over the bottle feeding duties until she's old enough to be adopted.
I really wanted to take her in--I thought she came along just as I'd been waiting for her--but my husband and I both work outside the home for a good 8 hours a day and neither of us could get away with bringing her to work. Plus, I want my daughter to be part of bringing in a family animal when we're all ready and this was going to be an exercise in frustration for her and constant vigilance on my part to keep her from hurting the little thing.
So thanks again everyone. I'm glad I took her in. It dropped to 30 degrees last night and she was all alone. Even if I wasn't the ideal parent I think I still helped her through a tough transition.