Hi Selena,
My family will be dining at the
T-REX Cafe for the very first time during our next visit to Walt Disney World and are very excited about it!
I would firstly recommend that you keep checking the online dining reservation system for the dates of your stay as cancellations do occur.
A second option would be to call the restaurant direct on (407) 828-8739 to see if there are any available dining reservations. As the T-REX Cafe is a non-Disney owned restaurant, I believe that only a certain percentage of their tables are booked through Disney Dining.
Lastly, you could always try simply walking up and asking at the restaurant itself on the off chance. If you still don't have any luck, there is nothing to stop you walking through the restaurant and having a look around the gift shop.
Wishing you a magical trip filled with memories which will last a lifetime!