If your Backpack was full at the time, the egg/pet will be put into your Bank. If that was also full, it might put it in your Shared Bank. If all three were full, the game would have given you a warning to delete something.
Check your backpack again, then your bank, then your shared bank. If it isn't in any of those places, go talk to Dalia Falmea again.
If you still don't have a pet, send in a ticket to Support. Be sure that you have room in your backpack or bank before you do.
