Should I respond in the future please let me know when your plans have changed or just in the future tell the owner I'm not available?

There are always going to be annoying people like this who ask if you are available and then never follow through. It really is up to you whether you want to deal with them again. So long as you don't hold a place open for their dog or change any preexisting plans, I would just respond that, yes, you are available. Archive the request and put it out of your mind. I wouldn't bother even following up to ask where they stand in the process. If they want you, they'll contact you and book it. Don't let it bother you. Just respond professionally--once--and call it a day.