Granddragon's first trip to the vet.

This is my granddragon, Peanut. My daughter "inherited" her from her boyfriend's sister-in-law when a toddler and an infant got to be too much and the mom didn't want to risk neglecting Peanut's care. So...my daughter stepped in as first-time dragon mom, ergo, I HAVE A GRANDDRAGON!!!!!!!!!!!

Peanut is nearly 4 and is going to the vet for the 1st time under my daughter's care. She asked me how to get her there. I thought maybe a cat carrier with a blanket in it for cushion and maybe a harness for when at the bet, but also said I really had no idea but knew who to ask. Pointers please? Thanks!