Greetings from the Florida Panhandle
First off, welcome to the Forums. We're glad to have you with us.
What you are asking is doable. There are a couple of sources out to rent an Airstream. I would call a couple of Airstream dealers, and see what they might have to offer.
You have located the absolute best source for all types of Airstream information. This is the place for all things Airstream.
I don't know if it is realistic to find an Airstream to rent in the Atlanta area. there is an Airstream Dealer near Atlanta. It is Camping World in Woodstock, Georgia. I would start by giving them a call and see what they might have to offer.
Your Jeep Overlander should be able to handle a 19 Bambi. You will need at least a 2" Class III receiver on the tow vehicle. You will also need to use some type of sway control/weight distribution hitch system. Additionally, you will need to install a quality trailer brake controller in your tow vehicle.
If you have any more questions, please do not hesitate to ask.
SuEllyn & Brian McCabe
WBCCI #3628 -- AIR #14872 -- TAC #FL-7
2015 FC 25' FB (Lucy) with HAHA
2005 Suburban 2500 Quadrasteer (Olivia) & 2011 Silverado 3500 (Fred) with Outfitter Truck Camper (Ethel)