Hi, Katie! How positively exciting to not only be taking YOUR first trip to Walt Disney World, but to be doing it with your little one! My last baby had her first visit at four months old, and I still look at the pictures all the time.
It's going to be warm in May, so shorts, skorts, t-shirts, and tank tops are probably fine for you. I keep a light jacket or sweater with me most of the time, because it can be cool inside some things, especially if you've just come from a water ride. Make sure you have comfortable shoes that have already been broken in!
For the baby, make sure you have light weight outfits, a hat, sunglasses if you think you'll be able to keep them on, sunscreen, and a light jacket or sweater. Have at least one extra set of clothes with you in the theme park for the baby - and keep at least a clean shirt for yourself as well. We've had baby bodily fluid related accidents that have sent me running to a shop for a clean shirt! Bring more diapers than you think you'll need each day, socks to keep the baby's feet covered, and if you are not breastfeeding, make sure you have enough feeding supplies (bottles, formula, etc.).
Extras I always took with me included a receiving blanket or two and clip-on fans that run on batteries and keep a gentle breeze on the baby even on the hottest day.
And don't worry if you forget something! The Baby Care Centers are life savers for traveling moms!
Have a great time - and take LOTS of pictures!