>"Should I consider diesel or gas?"
Diesel for sure... (1 ton single rear wheels for your trailer.)
>"I want the trailer to tow well but I also want some comfort and decent mileage for general use. "
You will likely get 12-14 mpg.
>"What brands are best? "
Heh... RAM/Chevy/Ford !!! Lots of people have different opinions !
I currently have a RAM 2500 with Cummins Diesel.
Works fine for pulling a trailer much like yours...
had it do do over again... would pick a 1 ton.
>"What cab configuration works well for our dog who will ride in the back seat area?"
We have 2 dogs. One a big Chesapeake (older dog) and 1 a 'Cowdog'.
The Chesapeake rides on the floor behind the passenger (on a blanket), the cowdog rides most anywhere on the back seat.
4 Door crew-cab... or a 'mega-cab' will do fine from all the mfg's..
>"Is leather seating out of the question with the dog?
Can the rear seats be lifted up and the dog ride comfortably on the floor? "
Rear seats usually fold 'down' to make a platform higher off the floor.
Chesapeake can't jump high enough anymore to make the higher platform.
Either conventional/leather... get a 'seat blanket' for the dog.
You can get a conventional seat cover... or one that reaches across to the front seats.
Here's a 'generic' photo from Amazon.