It's not impossible, but it is improbable.
One concern about a distance from SC to MT is that this trip might be too far for our PNP pilots to help. Most of our volunteers fly 250 miles at a time. They sometimes work together to complete longer transports by flying relays. The longer the distance, the less likely PNP will be able to help.
This distance might require too many pilots to be in the right place at the right time to relay over 1,000 miles in 250 mile increments to be logistically possible. I want you to have this information so that you might also explore other options of transport such as Operation Roger where long haul truckers offer rides on their trips.
Any transport of this distance requires multiple pilots & an overnight stay (at least 1 plus have some "just in case" options to hold the dog along the route). Winter weather (temps & snow) can be a major issue through the midwest/western states.
In the event you want to try, please go to the section titled: Ride Board: Animals Needing Transport and post your request.