K.M.
We just came back from a camping trip this weekend. We were rained out totally so I can give you some examples of what we wish we would have had, etc. Take a tarp to put under your tent before you put it down. Even if it doesn't rain the moisture from the ground will still seep up into your tent floor a little. We also purchased an inexpensive canopy from Aldi's that we used to cover our cooking/eating area. Small games for the kids that can be packed tightly (matching game, books, bubbles, silly string) We had a 4 hour drive to the campground so we also brought our DVD player (travel) and several DVDs. This ended up saving our weekend due to all the rain.
When it wasn't raining, it was 90 degrees and seriously humid. If you have an electrical site bring a small fan to move the air around. We weren't able to cook anything over our fire because of the rain so luckily we picked up a cheap electric grill/cooktop ($14) at walmart to cook on just in case. It was the only way we ate this weekend. Worth the investment and very compact to pack. These do get extremely hot so watching the kids is a must while using the cooktop.
A weather radio would have been nice because the campground was hit with 60 mile an hour winds and destroyed our canopy and blew our tent down, while soaking everything in it. Had we had more than a minute warning we could have packed up the important stuff instead so you may want to borrow one or just buy a cheap battery operated one. We also forgot a flashlight/lantern for our tent. It gets very dark at night when the kids need to be changed or go potty.
Keep all of your extra clothing in the car in case it rains, plus if it is humid you won't have damp clothing in the morning to put on. Take along flip flops or shower shoes because the bathrooms can get really gross and make you scared to walk in there.
Take a small clothesline or drying rack to hang towels on during the day.
For food, if you can take along fast food sized condiments it will save you a ton of space in your cooler. Tiny salt, ketchup, mustard take up a lot less room and require a lot less ice to keep cold. Breakfast bars in case you can't cook because of rain/heat. Our kids ate these most of the weekend because of our difficulty cooking.
My kids are just a little older 3 and 5 (plus I am 6 months expecting with #3) so some of the stuff that worked for us may not work for your 10 month old. Make sure you can keep hydrated. We all had heat stroke so if you are nursing or feeding your baby mostly from a bottle make sure to keep her hydrated.
I packed our meals (all the ingredients) in walmart bags and tied them shut and labeled them so that I wasn't rooting through the cooler for long periods of time. That way I just had to reach in and grab out the one labeled for that meal. It made it much easier to keep the cooler cold enough and we only had to buy ice once.
My kids only remember the fun parts so we were blessed with that, as for my husband, he isn't too excited to camp again for awhile and he used to be an avid camper. This was our first trip camping with smaller kids and next time (if there is one) we will have a better idea of what to pack and hopefully better weather!
Have a great time and make some memories!!