I've also got a puppy, and girls open me at occasions as well. All you have to do is to continue the conversation as it goes.
These are some common questions that I get:
* What's his name? *Giving the name*
* How old is he? *Giving the age*
* Does he bite? *Telling her the dog is a killer machine, etc (he's a tiny yorkshire terrier, i'm obviously joking)*
etc, etc...
So what do I do after I've answered all of her questions? I've already made her laugh a few times, depending on what she asked me (the questions above are from the top of my head).
So now just ask her back:
* Hey, do you also have a dog? (Yes/No)
* (Same common questions about her dog, bla bla)
* Jokingly tell her your dogs should fight til death, for money.
etc, etc...
Or if she doesn't have a dog...
* So this is your hobby? Walking up to strangers and petting their dogs? Wow, i actually thought of you as a bit more adventurous ...
(cold reads, routines or whatever...) * You think he's cute? Go ahead and take him. Just don't come crawling back when he trashes your house. You should see what he did the other day.... *insert dog story*
Anyways you get the catch. All it takes is to sit down and think of these topics to talk about. Obviously, apply them to your own dog. Don't steal mine.