All of the restaurants have high chairs, but I would suggest bringing some antibacterial wipes to clean them off before putting little one in there! We brought our high chair cover with us (we have a Jeep stroller with lots of room, so lugging it around wasn't an issue for us) and that worked out great. You never know who sat in there last, and the last time they were thoroughly cleaned!
Our daughter was a week shy of a year. The very best advice I can give is stick to your sleep schedule and routine as best you can. With naps, she was great about sleeping in the stroller, but we did make the mistake of trying to push it our first night, and paid the price. Our daughter fought going to sleep so hard (overtired, new environment, our bed next to hers, etc.), that she didn't go down til almost midnight, and was pretty cranky as a result the next day. Unless you have a wonder child, surrender to the fact you will have much earlier nights than you are used to at WDW, but the payoff will be an amazing trip for everyone. One day I could tell she had had enough of lines and rides, and we went back for a break and swam and napped, and she was great after!
We avoided fireworks like the plague because she despised them. As for characters, we showed her a TON of youtube videos before we left of what the characters looked like, and some days she loved them, some days not so much, but she always loved them from afar.
Our best purchase was a mini fan that attached to her stroller. It kept her pretty cool even when it was 95, and so many people asked us where we bought them because they wanted one for their child! You can get them on Amazon for about 10 bucks.