The new 2014 Ram 1500 Bighorn pickup has a payload of 1800 lbs. and a towing capacity of 10,350 lbs. and with the 5.7L V-8 and 3.96 gears can easily pull the trailer. With either a 1500 or the 2500 I would go with the 5.7L gas engine and the 3.96 gears.
A couple caveats to consider. The Ram 2500 pickup weighs 2,000 lbs. more than the Ram 1500 truck and that is weight that is being carried around 100% of the time whether towing or not. Second is that the frame on the 2500 is a lot stronger and may not need anything other than the factory tow package to pull the Airstream.
My GM 2500 with its factory hitch can pull up to 13,000 lbs. and have a hitch load of 1500 lbs. with a WDH neither needed nor recommended by GM. That would not be true with a 1500 pickup.
Check out the ride in the 1500 and 2500 pickups before you decide on either. It will be different and affect the overall pleasure of you and your passengers on long trips.
With any trailer you will want to add 1000 lbs. to the true dry weight (including all the batteries and AC and microwave, etc.) to have a ballpark loaded weight.
The 2500 fuel figure of 16 MPG has got to be a joke. My diesel 2500 truck averages 14.5 MPG with mixed city and highway driving. No way a truck with a gas engine is going to do better than 12 MPG.