Hi Colleen,
Birthdays are extra special at Walt Disney World! Everyone in my family has celebrated their birthdays at Disney many times, including both my daughters' 9th birthdays.
The free birthday admission you referenced was a special promotion called "What Will You Celebrate" that ran from January 1 to December 31, 2009. It was a very memorable offer; you are certainly not the only guest to remember it and wonder if it is still in effect.
Your daughter will be able to get a free "Happy Birthday" button to wear on her special day. Pick one up at any Guest Relations location. No guarantees, but I've found that guests who are celebrating birthdays often get some kind of surprise during the day, something like a free dessert or a special experience. At the very least, when she's wearing the button, your daughter will get lots of birthday greetings from cast members and other guests.
When our daughters were that age, we let them choose a special birthday lunch. One picked
Teppan Edo at Epcot, the other picked the
Plaza at Magic Kingdom. We also let them be in charge of what
FastPass+ choices we made on their special days.
Thanks for visiting the Disney Parks Moms Panel, Colleen. Please let us know if we can offer any other recommendations for your vacation. And wish your daughter a happy birthday from all of us!
Wilma