We took our DD for her 1st time when she was almost 9 months old. We stayed at Poly and had this great stroller by Instep, that also was a backpack stroller, she loved it. Disney is really good for families and babies, I was surprized at how many other babies we saw. Enjoy the baby care sations, but they can be a far way to truck.
As far as rides go the baby can go on almost anything the 4 year old can (as long as we are talking about a not to tall 4 year old:lol: ) Not goffys barnstomer or anything like that, but all other dark rides at MK. At that age they can even be easier then 2 or older when they know to be scared of snow white or pirates.
To make myself feel better I straped her into a side carrier the 1st couple of times, but it was not problem. Many rides can handle 2 parents and 2 small ones too. Babies love IASW! I am disapointed ours won't be able to see it on her 1st trip since it will be close for rehab then. TTA is a great slow down and relax ride, both your 4 year old and baby will like it (and it might put the baby to sleep, often you can ride 2 or 3 times in a row with out getting off if you want.
Our DD 1st ride was Dumbo, she loved it. Now it is a tradtion, always the 1st ride every trip. She is looking forward to our next trip March 2005 when we will have a almost 4 year old and a 6 month old baby (who is currenlty still inside me!)
We are heading to Vero Beach in 5 days, but don't plan on doing WDW, but who knows we might end up there! Have a great trip, take LOTS of pictures.