I've had rats and dogs, and really, the rat was more interested in the dog than the dog was in the rat. Reba learned to keep clear of Marcus' cage, lest he reach out and grab a pawful of her hair. She would pass by, watch him for a minute and then be on her way.
If your dogs are very prey driven, I would just keep the cage someplace higher up or put away where they might not be able to get at it or obsess over it. My setup was pretty large, so it just set in the living room floor, but it never got bothered.
Past that, enjoy the madness...lol. I miss keeping rats...I keep getting tempted to get another one, but I just don't know if it's a good idea at the moment. I just miss their personalities, and doing up the cages all elaborate-like. That was one of my favorite parts: changing around all their toys and shelves and hammocks. I'd love to build a massive cage someday (thinking maybe 5' tall or so) and just go nuts with things to climb and places to hide...make it as much as a decorative piece as it is a habitat.
SG2 CAC Discoe vom haus Huro, BH, AD, CD, TDI, CGC-A, CGC, HOT, OFA-Excellent, CERF
RIP Reba von Treue Freundschaft, CGC, TDI
May 11, 2005 - May 23, 2013