For information on transiting Canadian territory with a firearm:
Firearm Users Visiting Canada
For information on transiting Canadian territory with ammunition:
Explosives (http://www.nrcan.gc.ca/mms-smm/expl-expl/publ-publ/ima-ima-eng.htm#a - broken link)
Bringing your dog:
Canadian Food Inspection Agency - Health of Animals - Importation of Pet Dogs
You will require a valid US passport to enter the US from Canada.
Be sure to review the approved Canadian firearms storage requirements; hanging the Remington in the back window of the pickup probably isn't going to cover it.
Enjoy your trip and your hunt.