Hi M.! My daughter was about 20 months when we first took her to Disney. She'll love it though the poster who said she won't remember anything is right. Just be aware of that. However, my memories of bringing her there are priceless and she loves looking at the pictures of her at the princess lunch now that she's 3 and loves everything Disney princess. Just take lots of pics so she'll feel like she remembers it when all she'll really remember is looking at the pics from your trip. It will still be very special to look back on your trip many years from now.
We've flown with her several times now. I have always brought a sippy cup for her and have always been allowed to take it on. However, that is not the rule so they could make you pour it out. Just be aware that that is all they will let you take and they will make you open it and may even smell it. Don't take any other liquids including hairspray, makeup, water, etc. Pack everything in your checked baggage. Also, buy a new toy to introduce on the plane and make sure you have lots of snacks (without caffeine or too much sugar). Even if you give him juice be sure to water it down to avoid a sugar high on the plane (my daughter is very sensitive to sugar).
Now with Disney, my advice is to go with very low expectations. Let her needs guide you. Each child is different and has their own tolerance for stimulation. Disney is VERY stimulating. Make sure you have a good stroller with storage (you can rent them too), snacks and take lots of breaks. Don't stand on line for 45 minutes for a 4 minute ride. Try to catch the parades, go on rides like the carousel and it's a small world, go to shows. Magic Kingdom has a nice Pooh play area and another over in Toon Town. I'd spend most of my time in that park. They have the most rides for her. She'll love Buzz and Dumbo. Pooh and Peter Pan are not worth a long wait - try to use fast pass for them. Plus, there's nothing wrong with taking turns so you can each go on adult rides like space mountain. Try to use fast pass for those too so you can get on and off quickly. Just keep in mind that you can only use one fast pass at a time. Once you run it through a machine you can't run it through another one until you use the first one or the time expires.
Unless you need a relaxing day toward the end of your trip I'd avoid epcot. There's not much for her age (there's a water ride in Mexico similar to it's a small world and she'll LOVE Nemo but that's about it). Take turns and get fast passes for Soaring. It's amazing. MGM isn't bad, as one poster mentioned. They have several shows, including a playhouse disney show with mickey mouse clubhouse and Little Einsteins, and a restaurant with playhouse disney characters (play and dine - make reservations if you can). There are also very few rides for her at Animal Kingdom, though she'll probably love the lion king show, the pocahontas show and the nemo show (get to nemo early and try to get a good seat - it's a huge theater).
I hope this helps. Have fun! Relax and LET HER NEEDS GUIDE YOU and you'll have an amazing time.