I am happy you want to rescue a dog. Good for you!!
I do not have personal experience with volunteer transporation teams - my own term - but I do know that several rescue organizations use them quite sucessfully. Siamese Rescue for example (siameserescue.org) has what they call the Meezer Express to transport needy Siamese kitties to their new humans. They fly cats all over the world. At the moment, there is a cat scheduled to go to Scotland and Quarentine is almost up, 2 adult cats and two babies ready to come to the Siamese Rescue center in Virgina from Pakistan, and all manner of kitties riding around North America with volunteers. Often, donations are made specifically for an airline ticket or the person adopting the cat (adoption fee is $150) or the person pays for the fee her/himself.
There is one truck driver who has transported all sorts of Siamese kitties and even a few dogs across the United States. His cat travels with him - it's a cute story and he sounds like a try kitty angel!
Unfortnately, there are few drivers for the Meezer Express in Canada. I signed myself and some friends up for the Maritimes. <g>
If you lok into breed specific rescues, they may have a similar type of system.
But I have to also agree with the suggestion you look through other Rescues closer to home and inside the country - fewer problems with Customs and the various regulations that accompany that. Did you check out Perfinder and type in your postal code and then click National. It will list all the types of dogs you are searching for that are closest to you. It may very well turn out that Idaho is your best bet but suely there must be some small dogs for adoption in Alberta or BC or Sask???
Good luck! I hope you find a little guy!