Well, I don't think you'll have to worry about the payload too much if it's just the two of you and some pugs. The 2500 would be a nicer tow vehicle, but a 1500 could probably work for you too. Just check the payload and make sure the TW of the trailer, you, DW, the pugs, and other stuff fit in that weight.
My $.02 is that you should probably find the trailer you want first and then determine if the 1500 Suburban can tow it safely. It would stink to buy the 1500 only to find out you like that 26' TT that is a little tongue heavy, or over the tow rating.