Hi @Valentina96 , welcome to the group and to the wonderful world of pet sitting!
Petsitters come in all shapes and sizes and the good news for you is that there is definitely a section of this community that travel with their own pets
You may be interested to take a look at this thread from a while ago -
Is bringing your own pet on a sit allowed?
This is a photo we took last year in Brighton (UK) when we met up with our friends and full-time international trusted house sitters @marce (Marcela), Antonio and their very lovely dog, Leanordo who goes everywhere with them!