Your Play Store link is broken - this one works: https://play.google.com/store/apps/details?id=io.pawsible.Pa...
Definitely an interesting idea, and I'm probably the target market. Trust is obviously going to be a huge issue - what kind of required background checks are you implementing?
It also must be really hard getting something like this (effectively a social network) off the ground with enough users to be useful, especially when there's a geographic component. Have you considered focusing on a specific location first and growing from there?