Conversation goes well until a couple boring questions kill it off

You started off the conversation strong: you were funny, playful, and established some common interests with dogs. She responded fairly well to your questions, but they didn't really help create a deeper connection. And without that, she probably didn't want to put the effort into responding to your last questions.

My suggestion is ask questions that aren't generic - something that might catch her off-guard so her answers aren't prepared. People are more excited to answer these types of questions and their answers often tell you a lot more about who they are.