Nancy is correct. This would be a very long transport for the general aviation community.
Out of Minneapolis I would suggest using Delta Airlines (former Northwest). They have a great pet shipment program and the temperatures this time of year are within the limits at the departure and arrival cities.
I am a Delta pilot and I will be doing a Minneapolis to Abluqerque leg in November (I don't have the dates in front of me at the moment). I can escort your pup on this leg. You would have to go through the normal shipping process and pay the normal fees; however, I would be able to call you from Minneapolis to let you know your pup is on the flight I am flying and then call you again when we get to Abluqerque.
This is the link to the Delta Airlines website pet shipment. If the link does not work, google "Delta Airlines Pet Shipment"
Delta Airlineshttp://www.delta.com/planning_reservati ... /index.jsp
Let me know if I can help.
Sarah Murphy Case
Delta Airlines Pilot