imo its just great to pickup with a dog.

coz she is the one who will approach you indirectly by showing interest for your dog, so you dont look like you're into picking up girls or something...

she loves dogs/animals and this will open her soul(ie. omg he/she is so lovely, so cute) plus you as a dog owner and animal lover are automatically a good person, so she will know you two have a great thing in common

you have a great and long subject of conversation(about your dog and dogs in general), and its ok to bring back the topic of dog every time you have nothing to say

she will pretend to be more interested in the dog, so the dog will get most of her attention which is great if you're a bit shy
too bad i live in an appartment and it's to messy to rise a real dog, as about the tiny dogs i dont like them