Yes, you'll need either an extended driver's license or a passport to get into Canada, but please consider it at some point in your field target career. There are matches in Port Colborne and Ottawa throughout the year. I look forward to going to Port Colborne for their Canadian nationals in July and I'm trying to get up to Ottawa for a match at some point.
The border crossing isn't that bad either. Air rifles above 500 fps are considered firearms in Canada but it's not a big deal. There are forms on-line that you should fill out prior to your trip (HERE) When you get to the border it's really no big deal. When you get to the station explain that you are traveling to a field target match and that you have an air rifle to declare as a Canadian firearm. Have the paperwork ready if they wish to see it. They will then give you a yellow sheet of paper and tell you to park at the center median and wait for an officer to come to you. DO NOT PULL OUT YOUR RIFLES AT THIS TIME. Wait in or close by your car for one of their police to approach you and hand them the yellow paper and your passports/licenses. They may ask you questions about your gun, how fast it shoots, where you are planning on shooting, etc. no big deal just don't mention shrouded barrels or silencers. They will then ask where your air rifles are and may want you to retrieve them or just have you step back while they retrieve them. If you get them practice gun safety and be very aware of where the muzzle is pointed. They will want to verify the serial numbers on the gun(s), they will typically ask you more questions.
They will then tell you to go inside, pay your $25 Canadian, and you are then free to go. They take cash or credit/debit. The registration is good for 60 days so if you come back across within that time frame then you don't need to re-register your air rifles.
You can register as many air rifles as you want under one registration. However, don't push it. If you have more then one shooter in the car they tend to be a bit skeptical when you have multiple shooters and just one person registering them. We did this once and it felt like they were looking into my brain.
Coming back into the USA has been a crap-shoot for me. The first several years it wasn't an issue and I show them the declaration of an air rifle as a firearm and was good. However, in recent years I have been a bit frustrated trying to return to the US. It seems that at the mention of anything related to guns air rifle, pellet gun, etc. gets you to secondary even though air rifles are not regulated in the US. At one point I even had the US guard ask for proof that I purchased it in the US. Hello, here is the paperwork I DECLARING it on my way to Canada. Nope, go to secondary.
However, every time I go to secondary, they are very nice and when they hear your story they laugh, ask for your keys to verify the air rifles, and come back shaking their heads and rolling their eyes. Give you a slip of paper and tell you to have a nice day.
One time Eric and I were coming back to the US with about 10 piston air rifles in the trunk that were all broken. Before that I had tried many different terms without luck. The guard asked me if I had any firearms to declare to which I said no. He asked me to open the trunk and came back very angry demanding to know why I hadn't told him I had firearms in the trunk. "Because they aren't firearms, they're air rifles". I tried to explain that air rifles aren't firearms and that I had answered his question truthfully and wasn't trying to hide anything. He wasn't having any of it and sent us to secondary. I thought the guy at the desk was going to bust a gut laughing when I explained this to him while he rolled his eyes at the idiocy of the border guard sending us to secondary. He asked for my keys, verified my story, and handed us a piece of paper along with a "sorry about that" and said we are free to go.