A car is probably the most convenient way to get around - the park is huge, and things are far apart. Biking may also be an option, if you don't mind lots of hills.
Be careful if you choose to drive at night - moose are often spotted on the roads in Newfoundland, and collisions are common. An adult moose can weigh well over a ton, and hitting one at highway speeds is likely to be fatal. Moose are most active around dawn and dusk, so be vigilant if you're driving at those times.
