Welcome to the Dis! you came to the right forum for answers
Our first trip to WDW was when our DD was 4, so I know where your coming from.
With a 4 year old, your biggest enemy will be fatique (for all of you), so a break away from the parks will be great! As far as a stroller, IMHO it is plus/minus. Its great when the child gets tired and decides to take a nap, and with a top it keeps the sun/rain off the child. Park it early just behind the rope for parades and you can stand right behind it for an unobstructed view for all. Parking it and lugging onto buses can be a real pain and it is hard to move it around in the crowds. I ended up carrying my DD on my shoulders for most of the vacation.
You all will LOVE Chef Mickey's! Get an autograph book and take you camera!
Personal mist fans can help with the heat--esp. for DD!
Things to Do!
MK: Anything in Toon Town and Fantasyland. Big hint: Go to EE and make a beeline right for Dumbo! The lines and heat for the rest of the day can make it almost impossible. A majority of the rides are kid friendly everywhere.
EPCOT: You might consider staying away from: Mission Space, Body wars, Honey I shrunk the audience (That one got DD screaming her head off when the mice ran by her feet).
MGM: You might keep DD away from: Tower of Terror, R N Roller Coaster, and Star Wars. Make sure you see the Muppets and Fantasmic!
AK: You would probably want to avoid Dinasour (sp?). Great shows for kids in this park. Go early to The Lion King show, get your DD in the front and they may choose her to be in part of the show!
Don't forget you can use Kid Swap so you can enjoy the rides that you DD can't or won't ride. Good Luck and have fun!