Lisa
I know some members here have an Edge or Lincoln MKX and can elaborate on any issues they have had. I have a 2013 Explorer Sport, which uses a similar drive train, although my engine is different and while the transmission is of the same family it is more robust to handle the higher horsepower and torque.
I see your Edge is only a 2 wheel drive. I believe they are the only type that can be dolly towed - an all wheel drive model must be flat towed or on a trailer. This is from the Ford towing guide.
http://www.fleet.ford.com/towing-guides/You may have to look at the 14 year as the 12 and 13 only references towing on a dolly requires brakes. I don't think there is anything different between an 12 and a 14 Edge but you best check.
I have not had any issues towing my Explorer and it tracks quite well. The Blue Ox brackets are quite unobtrusive, although it did take some work to have it all installed. The only issue I have had is the coach throws up quite a bit of stuff and I have lost 2 fog lamp lenses; some kind of guard or protection will help minimize damage to the grill/body but the fog lamps are below where any guard attaches. I simply put it neutral, turn off ignition (i have push button start so no key in ignition) and go. Although limited to 65mph (hardly go above that anyway) and must stop and turn on and run it every 5 hours. I have a 12v line from the coach to the battery to help keep it charged while driving. I use an Air Force One braking system.
My only thought regarding a dolly is that it may get in the way at times when stopped somewhere for awhile, but that may not be an issue for you.
Jeff