I lived in Nfld for 9 years (two different stints when in the Airforce) and can attest to the number of Moose there - if we didn't get one it was because we didn't hunt that year.
The population has reached "pest status" now in some of their (WMU's - don't remember what they call them now) and there is more tags then hunters.
Non-residents "must" use a guide. There was a few guide services there but they were few and far between and don't personally know anyone who used a guide service down there (so can't give a first hand yay/nay for anyone in particular). If you go to the Newfoundland and Labrador website (advertising the province you can get guide listings there).
(edit for some info on their "guides" - to be a guide down there you only need a hunting licence, first aid certificate and a boaters card - so if you need to be really careful that you don't end up with "bubba" who is just trying to make a couple of extra bucks by "walking some Mainlanders through the bog")
The place is expensive to get to and not much there when you do get there so absolutely would have to bring everything with you that you need (as far as ammunition etc).
And just looking up their hunting guide, a non-resident Moose licence is now $502
But if you absolutely want to shoot a moose and have a fat wallet, it's one of the top places to go.
Hey, if you throw in another 600 or so bucks, plus the cost of the guide, you could add a caribou to your adventure.