Welcome aboard! Don't for get to check out the Full Timers Forum here too, a lot of good knowledge and experience. I know over the years of several traveling RN's that have done the same thing. Seemed to work out well, many hospitals had basic hook up's too I've read.
I would suggest the dually that Voltage 3895 is over 42' of trailer with a hitch weight of over 3,000#.
As for the dogs, ours road in our Raptor and did just fine. In many ways probably more relaxed back there then in our truck, but at the time we had 2 kids. If I didn't have kids I'd have them in the truck so I didn't have to run the AC for them on hot days.
