In Newfoundland hundreds of moose have been taken and are still taken with a .303 British (usually 180gr). Also popular are the .30-30 and .270 (average shot under 100yds).
So you are good to go with what you have in terms of power.
However, equipment aside, if you drew a moose tag around Drumheller (wide open), then you might want to get more comfortable at 200 yds. Moose might not have too keen of eyesight but that snout can pick up scent easy on flat windy prairie. As it has been said many times shot placement is paramount and not believing in your skills at longer ranges may handicap you when the time comes to sqeeze that trigger.