B.M.
I have always used carseats for my children...it is always recommended for children under 4....they are safer, often more comfortable and kids are much less likely to get up and down and move around when in their seat...plus you will need to use your carseat when you arrive and checking it as luggage is taking your chances ...if your seat is lost then you are stuck with a child and no seat (and don't even think about renting a carseat/the rental companies seats are downright scary- old, nasty, broken, unsafe!)....when I've flown alone I put my seat- a large Britax Marathon (most seats fit and are FAA approved..there is a sticker on your seat stating this) in a bag with wheels and attach the bag with a bungy cord to my stroller and put my child(ren) in the stroller....airports are so busy...other travellers are always running over kids and it's way too crazy for me to consider letting them out of the stroller/and any delays will be easier to handle if have the stoller..I've heard that often the Disney strollers are not available (sold out) on some days, there is no guarantee....and for a 3 1/2 you definitely want one for Disney.
As for the booster...at 3 1/2 she's really much too young for a booster (car seat techs advice 5pt harness use until at least 5 or 6) and boosters are not permitted to be used on airplanes.
Hope this info helps...if you don't bring the carseat on the plane it's highly recommended to at least gate check at the airplane door with the stoller so you'll have it although if you lug it all the way to the plane I'd use it on the plane.
B.