Not to be insensitive, but that is the reason I wanted Yorkies in the first place - rat catchers!
I ended up with a poodle (long story, but it all worked out perfectly) and figured I wouldn't have a rat dog for a while. Well, I was wrong. I mowed the yard (over an acre), took a shower and was relaxing on the back porch in my shorts, all nice and clean when Bug (toy poodle) jumped in my lap and dropped the present he caught and killed for me. A large, freshly killed field rat. I squealed like a little girl, grabbed the rat by its tail and flung it in the yard, much to Bug's hurt expression. lol I am by no means squeamish at all (I work in a trauma center in a bad part of town for doG's sake!), but I never expected my beautifully groomed, bed buddy cuddle Bug to seek and destroy a HUGE rat and then to drop it in my nice, clean lap on bare legs. LOL
Bug is now teaching my Yorkie kids to hunt. I am quite proud of my crittering dogs.
(Now, bunnies would hurt my feelings, but rats and squirrels, not so much)