Well we don't have Gophers in Ontario but we have lots of the bigger Groundhog. Pound for pound the Groundhog is the tughest little critter around and can absorb a lot of 22 rimfire unless you hit him in the head.
There isn't enough hitting power in a 22 LR to shoot Groundhogs consistently beyond 75 yards and even then it is marginal.
As for Crows, hunting a crow with a 22LR is an exercise in stalking and knowing your rifles capability in excess of 100 yds. Crows know the shape of a rifle and stay out of range. You can hold and aim a broomstick at a crow and he'll sit there and laugh at you ut as soon as you produce a rifle he's off like the wind.
Reports from big time groudhog shooters say that the .17 based on the 22LR doesn't have enough killing power on a Groundhog at 100 yds and the animal often gets away down his hole and dies in agony down there.In that case go for a 22 mag or the 17 equivalent size.
For Rabbits and Grouse you need a 12 ga shotgun. Grouse can erupt into full speed flight and using a 22 to shoot at them can be dangerous at longer distance to someone else.
J