Not the gun. If you can’t guarantee a clean shot don’t take it, even vermin deserves a humane death. Besides, 12fpe is overkill for ratting, a close range gun should be in the 8-10fpe range as you have to consider where the pellet goes afterwards. I’ve even seen people use pistols with shoulder stocks (6fpe).
Also, do yourself a favour and make sure its legal, a chrono costs less than a firearms offence. Find out if someone local has one you can send few pellets through, if it’s hot then its no harder than taking the spring out to keep it legal.
Lastly rats are a bugger. My folk got some, they were happy enough with mice in the garden but rats were another league. Burrows everywhere. Poison sorted them out but be aware if there is something worth having they could well come back. It was the bird feed they were after in our case as well (plus chickens didn’t help).
Oh, another thing, they can’t see in red light. I’d be taking full advantage of that fact to track them, they are creatures of habit.