It depends who you are flying with... you will have to contact the airline and see if they will allow you to have him on the plane with you, if not you'll have to see their rules on storing him away.

I just checked Air Canada's site and it appears that you can't have them in the cabin anymore and there are specific rules as to when you can store them as cargo (due to increased passenger loads, temperatures, aircraft type etc.) To read more
Click~Here.
I know my friend flew on West Jet a little while back and the lady beside her had her small parrot on her shoulder for most of the trip... I just checked their site and they do allow you to bring one pet with you in the cabin as long as the proper carrier fits under the seat... but I don't think that West Jet flies NB to NFLD.
It would probably be best to call up all the airlines that you could fly with and see what their rules are on bringing a bird with you.

Good luck!