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It is not that big a deal.
Obviously you need an ATT to take it to a border crossing and return home
Then you need to list it on your NIA6 to BATF - if they approve you are good to go
Then you need to check to make sure where you are hunting legally allows handgun hunting. And as long as you are legally able to own a handgun in Canada most states will let you hunt there. But not all --- so do the research with the state DNR you plan to go to.
I have hunted deer with a handgun (by buddies gun) in Michigan (He is from Illinois)
Bottom line is - check with the DNR for that State.
I went through the process and got a USA Temporary Firearms Import permit. I listed about 6 handguns, and got approval for all of 'em. So if you were going to a US state that allowed handgun hunting, you'd be good to go.