If ever there was a transport that should be done via commercial flights this is the one.
We have suggested that longer flights need to be commercial flights, but as pilots we only reference the problems with flights that are relays. Apart from the coordination between the multitude of pilots involved, along the route all the pilots can expect that at least some will have to deal with weather, mountain crossing, and long legs due to the sparse population beneath areas along the route. All of those potential problems should not be minimized.
Unspoken previously is the true cost of such an effort. I would guess with fairly fast planes the time enroute would be 15 hours, and would entail about 6 400 mile legs. Planes capable of the speeds and altitudes required likely cost in real terms about $200 per hour to fly, and since each pilot will deadhead an equal number of miles as he did to transport the total contribution will not be 15 hours, but 30 hours for a cost of $6000.
We are blessed to have so many giving pilots as we have, but at some point we all need to recognize that we have to weigh the cost and compare it to the benefit. Having said that, There are times we all have to ignore the practical side of things and look at how we can leverage something that might not be reasonable into a big plus. Clearly this transport involves a pup that can epitomize what pilotsnpaws is all about. If a group of pilots can put this together, even if it involves combining the total trip with ground or commercial transports those involved should get the media to cover the transport to emphasize the need for spay and neuter programs, our need for more volunteer pilots, the threats to general aviation, and to emphasize the kindness of our pilots.
No matter how this works out, good luck. Be persistent.