We went camping with DS when he was that age for five weeks. We had two adults and him in a four person tent and we were comfortable most of the time but sometimes I went a slept in the car because they boys flip and flop and DH snores awfully. If we'd had two more adults I would have suffocated. I think they make those measurements with Vietnamese women in mind or something, not the average sized European for sure, so unless you are all quite petite, I'd go for a bigger tent. The four man tent is just about right for queen sized mattress. If you think four grown ups and a toddler on a queen sized mattress is a good idea, then you'll be fine.
Bring ear plugs.
Bring a hammock to string up between the trees.
We brought a play pen with us to keep DS safe while we loaded up the car (he is a wanderer and he used to wander down to the lake edges and over to other people's campsites and behind cars and...OY!)
Bring warm jammies and a hat for the night time...you will probably find though with all those people in such a small space that you might be kicking off covers in the night, too.
Food is dependent on how long you are going.
We brought powdered milk and UHT milk, canned and powedered soups, rice, pasta canned beans of all sorts. for DS and DH we also brought canned chicken and tuna, but you may also be able to fish for and eat fresh fish which even though I no longer partake in I can tell you is just the best thing on earth! I would bring oil for cooking, Peanut butter, bread, potatoes. canned tomatoes, onions, garlic (and lots of it!), salt, pepper, sugar, coffee, hot chocolate mix, marshmallows for roasting...favorite dried herbs and spices. Add water pancake mix, and powdered eggs. Some hard cheese like parmesean and a grater to add it to food (if you bring it pre-grated you will probably see it go off after a couple days out of the fridge, but a block can last longer). Nuts and dried fruits and veggie crisps are all good stuff too. Edemame is also a good snack for camping. Vitamins and pepto bismal
equipment: I would bring a round grill to put over a fire, a lighter and fluid, newspapers for kindling starters, a metal kettle for boilng water, an aluminum pot a griddle like pan. A spatula, metal tongs, a good knife, a cutting board, a pitcher and plastic cups, forks knives and spoons (you can get these little mess kits at camping stores I don't know how much for but they fold up nice and neat with a bowl a plate a fork spoon knife combo, and a collapsible cup...I think I remember mine costing like 8 dollars but that was in the 1985.) Cleaning supplies for sure. Biodegradable please.
You will need apart from a tent, a ground tarp and a if it is rainy where you are going to wouldn't hurt to have an additional tarp strung up between trees over the tent and another one for over your kitchen and eating area. A hammock is a great thing to bring. Not only will it give you a place to hang out with DS apart from the tent (in case you friend wants a nap for example) but is also easy to pack up and travel with.
Plenty of picnic blankets for spreading out on the ground and relaxing.
If your trip is long it might not be a bad idea to invest in an inflatible mattress and pump to put in the bottom, because if you don't you might find wearing a toddler all day and sleeping on the ground all night will take it's toll, no matter how young you may be.
I don't think you'll need to bring much in the way entertainment for your LO. I brought a few books for bedtime stories and his stuffed animal. That was it. As I mentioned before he was a wanderer and fascinated by the natural world. You could give him a plastic shovel and a bucket and he'd go off exploring with his dad and come back with a virtual terranium full of wonders and five new friends while I made dinner.
Definitely bring suncream, bug spray and well stocked first aid kit especially if your LO has enever been stung by a bee...you don't want to find out a thousand miles from anywhere that bees, ants or plants make your LO swell up like a Macy's parade balloon, and not have the necessary stuff. As it happens for us it was DH who we discovered had a rather nasty allergy to a particular type of caterpiller...thank god we had those antihistamines...bought us time to get to the local clinic for a shot of ardenilin. Sun hats, long sleeve light weight tops. Rain gear.
Flashlights and a latern.
Toilet paper and shovel or a big heavy duty plastic bag to take out what you bring in, IYKWIM. Definitely make sure you bring trashbags to haul out the grabage you bring in that can't be buried or safely burned.
Flip flops and sneakers and hiking boots, warm socks, and cotton socks several pairs. A bathing suit and towels. a small camera to document it all. Binoculars if you have them or can borrow them would also be cool. I bet the wildlife there is to die for!
Obviously all of this depends on how far the park campsites are from civilization, how long you intend to stay, how far in you want to hike, and your own comfort levels, and money. You have me thinking of our upcoming trip now, I can't wait for this summer! We're taking DD on her first camping trip down to Tayrona Park on the northern coast of Colombia. Should be a blast!