First of all, you need to know that Canada has some of the strictest gun laws in the WORLD.
Yes you can bring a handgun, rifle or shotgun into Canada, but there is lots of paperwork and it will cost you a few bucks. They also have plenty of restrictions, so you will want to compare those to what you intend on bringing with you.
No, you can not carry your handgun in Canada, so telling them you will use it for protection is the wrong idea. You will have to come up with a much better rason than that. You will need to make some phone calls and fill out some paperwork before making the trip. The process would be much easier if you were just going through Canada to hunt in Alaska.
I have never attempted taking a handgun into Canada, but my Uncle and Cousin's tell me it's a huge pain, and probably not worth your time. When members of my family go hunting up that way, they refer to these websites.
http://www.canadianembassy.org/government/guncontrol-en.asp
http://panda.com/canadaguns/#preface