Pilots N Paws has basically no barrier to entry. The main challenge is that the organization of transports is entirely between the person requesting the transport and the pilot(s) involved, and in my experience it's often a lot like herding cats to get things squared away.

I've only flown a handful of transports since starting five or six years ago, but that's mainly because my weekend availability + the difficulty of booking rental aircraft on short notice limits my usefulness. Given the organizational issues mentioned above, it's pretty common for transports to come together at the last minute, and by then typically I can't get an airplane.

If you do get into PnP transports, I definitely recommend having a helper along, especially if it's a large dog that can't be crated in your aircraft. Once I was flying a husky and I decided to do it alone. Thought I'd secured the dog in the back seat, but about the time I reached the runup area he joined me in the front seat. Ended up having to request a taxi back to re-secure. Only slightly embarrassing...