The rain will do the trick. She'' forget about the rat in a day or two. She'll go back to chasing squirrels (that she will never catch).
If she deserves a treat, then I should get one, too. She sniffed it out, but I was the one who dispatched it.
Like you, I have no problem with wildlife, including rats... as long as they stay away from my house!!! Since I live a few hundred yards/meters from a 3,000 acre cattle and horse ranch, we get all kind of things wandering into the neighborhood. Rats, coyotes, bobcats, raccoons... all kinds of animals. We also have feral cats, and they deal with most of the rats. In the hottest months of summer, a few of us in the neighborhood put big bowls of water out for them. No food! They will lose their hunting instincts.
BTW, I live in a city with 250,000 people, an IKEA and a Hyatt Regency hotel, and yes, a 3,000 acre ranch. Only in Texas.
CD