Yep; it's a way better case for a coordination website. That site is Rover, which to my knowledge is doing just fine. (Wikipedia suggests they cleared $30 million in revenue last year.) They offer dog-walking too, but are probably a bit safer because the boarding offer is a good incentive to just stick around and use one site for everything.

(Rover also provides insurance on each deal, a very un-Uber approach that's actually more protective than most low-tech arrangements.)