June, welcome to WDW.
Our daughter when she was 8 1/2 month old last Dec. It was a great trip and we all (baby husband and I ) had a wonderful time.
We almost never get a sitter at home, but by the end of the week I was wishing we had at WDW for at least a few hours. Our next trip March 2003 we are considering getting a in room baby sitter for a few hours. It is pricey. I have never heard any baby things about Fairy Godmothers or any other babysitting on Disney.
There is a lot to do with the baby, child swap works well for rides.
Don't leave your baby at home to go to WDW. Every child you see you will miss yours. If someone is considering a trip with out children plan one to a non child place.
IMO 9 months is a great time for a babys first trip, they are still portable, able to enjoy some things and Disney is very baby and child friendly. (As long as you plan on going again too when they are older and will enjoy it even more, and accept there are some things you can't do with the baby and are fine with that.)