DUI is a felony in Canada. Gross Misdemeanor in the US. Therefore in Canada' s eyes, you are a felon and therefore unable to posses a firearm in their country. You need to get this cleared up BEFORE you arrive at the border. I do believe that you can " buy" a waiver for $200.00 (cdn) You need to contact Immigration Canada and find out what they are going to require from you. Most of the time a printout of your criminal history is required with the waiver packet. You can obtain your history through your local county sheriff' s office. They will most likely charge a small amount to give this to you. If you click on the link that was provided above you should be able to find the phone #. Best of luck to you!
Here is the link to Immigration Canada:
http://www.cic.gc.ca/
Phone # for the Canadian consulate office in Detroit
313) 567-2085
If you have a Canadian Embassy in your state you should call them. They can set you up with this stuff before you go on your trip.