From DL website. I really think it will be up to who ever you get at security and then again at the gate and at the restaurant. Why not just tell the restaurant its her bday. They will bring her a small cupcake with a candle and sing happy birthday. You can save the cake for the hotel or outside the park.
Dining – Frequently Asked Questions
Q.
Can I bring outside food and beverages into Disneyland Park or Disney California Adventure Park?
A.
Guests are allowed to bring outside food and nonalcoholic beverages into the parks for self-consumption, provided they are not in glass containers, do not require heating, reheating, processing or refrigeration and do not have pungent odors. Inform a Security Cast Member of any food items when you enter the park.
You may also enjoy your own food and nonalcoholic beverages in an ideal setting at the complimentary
picnic area—conveniently located outside the Main Entrance to
Disneyland Park.