Hi Charles, welcome to planDisney!
How fun! The
Disneyland Resort is one of the best places to
celebrate birthdays. Be sure to visit City Hall on
Main Street, U.S.A. in
Disneyland Park, or at Guest Services in
Disney California Adventure Park to pick up your complimentary birthday button for your child!
But back to your question, children under the age of three do not need a
theme park ticket to enter the parks. As long as your child is still two years old when she first enters the parks, she will not need a ticket for the length of your stay!
AND! I do want to mention that the
Baby Care Centers are amazing and worth a visit! My wife and I used them often for our little ones. They offer a clean and comfortable facility with changing rooms, nursing rooms, a feeding area with high chairs, and more. At Disneyland Park, it's located at the end of Main Street, U.S.A., next to
First Aid. At Disney California Adventure Park, the baby care center is located next to
Ghirardelli Soda Fountain and Chocolate Shop, across from
The Bakery Tour in Pacific Wharf.
I hope you have the most wonderful time celebrating your child's birthday!
See ya real soon!
Jin