Again, it sounds like a CNM is what you are looking for. Because a CNM is registered with the Israeli government for homebirth, you will have a very easy time getting this information from her that is both current and applicable to your situation. So what I am about to tell you was current and legal at the time I homebirthed with a CNM, which was about 3 years ago. The laws are likely about the same now, but when you interview CNM's they will be able to give you all of this information totally up to date.
Anyways, with a CNM (certified nurse midwife) you will birth at home and the CNM will fill out all of the paperwork you need for a homebirth and also give a copy of her stamp/license and you will take all of these documents to the misrad hapanim (I believe that's the right one, but the CNM will tell you) and simply give the paperwork to them and they will register the baby and give a birth certificate in Hebrew AND ENGLISH (FOR FREE...provided you request the English one in addition to the Hebrew, which you will need for foreign passports...so don't forget to ask for it!). I don't think that there is a time limit. With our ds we went to have him registered something like a week or two after his birth. This was after his brit milah for certain (so he was AT LEAST 8 days old, and very likely had a few days to heal). I know this because we do not announce the name until the brit, and so there was no way I would have even considered taking him to register him and give out his name before that time.
The downside is that the mother and baby MUST be present for registering (again, check with your CNM to know if that law is still in effect).
At the time that I had ds, it was also "required" that a peditrician see the baby within the first 48 hours. Some women take their children to a hospital for this. I highly recommend against it. Not only will you get a ped on call, but hosptials are notorious for being pissed off that you had a homebirth and not "trusting" that everything is okay. Also, many hospitals have rules that when you arrive with a baby after a homebirth, they need to take the baby away from you for observation...this could be for as little as an hour but usually becomes much more as they say they "can't be sure" that all is well and typically demand that you check yourself and the baby in...or even worse, ask you to check in your baby and then tell you you need to leave him/her overnight for further obeservation. Not good. Also, since a hospital is a place for sick people, it is very common for babies to pick up germs and viruses from the hospital while there, which means you will be coming back to deal with that about a week or two later...or just dealing at home with a sick baby.
But there is no need to do this.
You can take your baby to your local kupah peditrician or, better yet, hire a ped to come privately to your home. MOST if not ALL CNM's work with peds that come right to the home. The average cost for this back 3 years ago was 500nis. The ped comes right to your door, takes a look at the baby, confirms that all is well, fills out a form, and you submit that form to the misrad hapanim when you go to register the baby. Again, I dont' know if this is still required, and it may not be.
As for me, it was very simple. I had a CNM, birthed at home, and my CNM called one of the peds that she works with and he came over within a few hours to check out the baby. It was a 20-30 min visit, he talked to me about nursing and a lot of other things that I really didn't need or care to talk about (I was not a first time mother and rather well-informed and confident, at that, but some might find it soothing). We paid him 500nis, he gave us documentation that he was there within 48 hours of the birth and that was the end of the story. We took all of the papers to the misrad sometime after our son's brit (within 3 weeks, most likely) and they asked "why did you have this baby at home?" We said "because we wanted a homebirth." and they said "okay" and that was the end of it. They gave us his birth certificate on the spot. Then we asked for an English one, which they also gave us. Once we had this documentation we were able to take passport photos and register him for a passport with any country he was eligable to register for.
So it was very very simple.
This time, I will be B"H working with a lay midwife. Aparently this is slightly more complicated as it will "look" like I just was irresponsible and didn't get proper medical care and then the baby just came out before I could get to a hospital. Either way, my understanding is that so long as I have a note dated sometime in the 8th or 9th month from an OBGYN saying that I'm pregnant and expecting on my due date and then a note after the birth within 24-48 hours from an OBGYN saying that I had a baby within the past 24-48 hrs (they want to make sure that the baby is, indeed, YOURS!!!) then I have met the requirements. Aparently it is not NECESSARY to have a note from a ped, but it is BETTER to have one in this circumstance. So I will also need to hire a private ped to come to the house within that time period to state that the baby she is seeing is less than 48 hours old and the baby's condition. I will then take the 2 letters from an OBGYN (one from the end of my pregnancy and one from the immediate post birthing time) and the letter from the ped to the misrad and tell them that I had the baby at home before I could get to the hospital (if they ask "why" I had the baby at home). Aparently this meets the government criteria for homebirth in the event that it is NOT with a CNM and there will B"H be no balagan provided I have those documents and they will simply register the baby and all will proceed as above. I am TOLD that it is helpful to have an ultrasound of the baby as well to show them, though I am opposed to this on principal, because my medical records are not the misrad's business and private. But, as this is Israel, I don't think that matters to anybody but me. Aparently it is BEST to have the ultrasound performed in the 8th or 9th month of the pregnancy, as this PROVES beyond a doubt (to the misrad, anyway) that you were pregnant right up until the very end, and that you got proper medical care (by having an ultrasound, don'tcha know!) I actually DO have an ultrasound, of the feet and hands, ironically, from early on in the pregnancy and won't be having another ultrasound after that unless there is a medical indication that I should (which will either be made apparent to myself or my midwife), so the one I have will have to do.
At any rate, its not as complicated as it sounds. Many women are doing this every day. There are government regulations in place for it. With a CNM it's perfectly legal...and you know what, even without a CNM, having your baby at home and not making it to the hospital in time is perfectly legal, too. B"H all will be well.