I don't want my girlfriend to get a puppy
Why don't you want her to get a puppy?
She promised to take care of it but she's not reliable
Maybe you should talk to her about your concerns. You shouldn't really try to dictate whether she can get a puppy or not, though.
I just really don't want her to have one.
It definitely sounds like a discussion you need to have then. Having a pet is a huge responsibility.