Here are the specific height requirements for the attractions at both parks so you can be prepared:
UNIVERSAL STUDIOS®
Jimmy Neutrons Nicktoon Blast- Must be at least 40. Persons under 40 must experience this attraction from an adjacent stationary location.
Back To The Future The Ride® - Must be at least 40 ; 40 to 48 must be accompanied by an adult.
MEN IN BLACK Alien Attack - Must be at least 42 ; 42 to 48 must be accompanied by an adult.
Woody Woodpeckers Nuthouse Coaster® - Must be at least 36 ; 36-48 must be accompanied by an adult
UNIVERSALS ISLANDS OF ADVENTURE®
Jurassic Park River Adventure® - Must be at least 42 ; 42 to 48 must be accompanied by an adult.
Pteranodon Flyers® - Must be at least 36 ; 36 to 56 must be accompanied by an adult. Guests over 56 must be accompanied by a guest meeting this requirement.
Dueling Dragons® - Must be at least 54.
Flying Unicorn® - Must be at least 36 ; 36 to 48 must be accompanied by an adult.
The Cat in the Hat - Under 48 must be accompanied by an adult.
Caro-Seuss-el - Under 48 must be accompanied by an adult.
One Fish, Two Fish, Red Fish, Blue Fish - Under 48 must be accompanied by an adult.
Dudley Do-Rights Ripsaw Falls® - Must be at least 44 ; 44 to 48 must be accompanied by an adult.
Popeye & Blutos Bilge-Rat Barges® - Must be at least 42 ; 42 to 48 must be accompanied by an adult.
Incredible Hulk Coaster® - Must be at least 54.
The Amazing Adventures of Spider-Man® - Must be at least 40 ; 40 to 48 must be accompanied by an adult.
Doctor Dooms Fearfall® - Must be at least 52.
Storm Force Accelatron® - Under 48 must be accompanied by an adult.
Make sure to bring her bathing suit and a towel. There are fun areas where kids can get wet in both parks. IOA, at first glance, might seem to be less little kid friendly, but there are not one, not two but THREE kids fun areas; Me Ship the Olive at Toon Lagoon, Camp Jurassic at Jurassic Park (watch out here though, a little one could get lost VERY easily), and If I Ran the Zoo at Seuss Landing. All three of them have wet potential
As for the birthday question, I know that Circus McGurkus Cafe in Seuss Landing has a birthday celebration each day. I think it's around three o'clock but check your show schedule when you arrive at the park.
Hope this helps. Have a great time!