Quebec and Ontario both have non-resident moose hunts. New Brunswick has a season too, but it is very short, and you usually need preference points. Newfoundland and Labrador both have very good populations, and over the counter tickets for non - residents. Are you planning to try this yourself or with a guide? These are huge critters, and you are sometimes required to bring them out intact. Even if not, it is possible for an entire carcass to go bad before you are able to get it out, if not prepared.
An outfitter in NewFoundland I have contacted several times that offers great hunts and is highly recommended is Patey and Sons, Ltd. One of these days....