Hello Nasiba! You must be so excited to be able to celebrate your son's birthday at Walt Disney World! Although you may have trouble finding a character meal at this point, don't worry - there are other fun places you can dine. You may want to check out the
restaurant page on disneyworld.com to get an idea of what is available. A couple of fun, non-character dining locations you may want to consider are T-Rex Cafe, Whispering Canyon or 50's Prime Time Cafe. The Rainforest Cafe is also a fun choice and they they do have availability for the 19th (I checked the Animal Kingdom location).
When booking your reservation, you can also add a birthday celebration and purchase a cake for dessert. You can also call the Cake Hotline at 407-827-2253.
Also, make sure you son gets a birthday button to wear on his special day! You can obtain a button at the front desk of your resort or at any guest relations window at each theme park.
I hope your son's birthday at Disney is fun and magical! Diane