Advice for a grossed-out city boy

So, I come home from work yesterday to find a dead rat lying in the middle of the living room floor, and two dogs (aa lab-corgi mix and a beagle) smiling and wagging their tails. The two supposed culprits do have access to the backyard via a dog door, and the victim was stiff as a board, so my best-case scenario is that the rat was dead when they found it and they graciously brought it in so that I could give it a proper burial.

Anyway, never having had to deal with the likes of this before...do I need to worry about anything? (With the dogs, I mean...the fact that I may have rats in my house is a seperate issue) The rat was not chewed up or anything, assuming it WAS alive when they found it, they're both current on their rabies vaccines, and they haven't exhibited any strange behavior since yesterday. I hear tell that things like this are fairly common, am I just being a nervous nellie?

Honey, they brought it in for you as a dinner offering. Bon Appetit!

My cat brought in a dead rat and we have lived to tell the story. I would let it go.

and you would not want your dogs getting any of that.
Also..if there is rat poison around and the rat ingested it, and then your dog bites the rat, they could get very sick..it would be very bad. Rat poison is basically an anticoagulant, and if ingested could cause internal bleeding.

See if there is anything nearby that could attract the rats. If so, see if you can get rid of it.

Eating the rat would.