Not that it wouldn't work, it's just a bit much in my opinion. Especially on a critter you want to save the pelt on. The V-max's can be a bit distructive, but maybe not too bad on something the size of a coon. A head shot could likely take the head off if the range is right.
Plenty of people use them on coyote if you limit your range, others will tell you it's a bit light for one. I have never done it to be honest. I got mine for target shooting and a little varmint work. I would suggest the 20 gr. XTP's for dogs as well because they penitrate better.
Like I said, I'm not trying to talk you out of one because they are awsome little guns. Especially when you can get a savage or marlin rifle for $200 or under, a decent scope and shoot 1 inch groups at 100 yards on average, with no drop!
If I were you I'd get a .17 if you want one and keep the .22 for coons, what you have is a great little coon rifle in my opinion. Cheaper and quieter to shoot than the 17HMR. Now if you want to blast a coon out of tree at 100 yards away, the 17 is your gun

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Paul