They don't have "Christmas Parties" in DLR like at WDW.
They do have the Happiest Birthdays on Earth party at the Plaza Inn.
Here's a description:
Where: Plaza Inn,
Disneyland
Cost: $10 per person (free for children under 2). Premium Annual Passholders get a 10 percent discount
Age Range: Geared towards children 12 and under
Priority Seating: Call Disney Dining at (714) 7813463 or stop by the Plaza Inn or City Hall
This birthday celebration appeals more towards children than adults, though you can usually spot several youngathearts joining in the spirit. The structure of the party has changed little since it debuted three years ago at the Plaza Inn. The price includes a blank cake with sprinkles and frosting, punch and a plastic birthday drink cup, a party hat and a special sticker.
There are lots of other free things she can get for her birthday.
Here's a link for you:
http://www.mouseplanet.com/articles.php?art=mm050412lp