Note that the completion of vaccinations and vet forms can take 3-4 months, so if you want to take your dog to Norway, plan early. Tattooed dogs and cats won't qualify after 2011 in favor of microchips.
The most important thing to know when taking your dog to Norway is that three types of pet regulations exist depending on whether you enter Norway from Sweden, from an EU country, or from a non-EU country.
Bringing your dog to Norway from the EU: First of all, get a EU pet passport from your vet. Your licensed veterinarian will be able to fill out the EU pet passport as required. To take dogs to Norway from within the EU, the dog must be vaccinated for rabies at least 21 prior to travel, tested for rabies antibodies by an EU-approved lab, treated for tapeworm, and possess a pet passport showing the information. When arriving in Norway with the dog or cat, take the pet to the customs upon arrival (red zone).
If you take your dog into Norway, coming from Sweden, you are exempt from all requirements.
Bringing your dog to Norway from a non-EU country: Requirements for pet travel are slightly stricter. Like travelers from the EU, you should also get your dog a pet passport if at all possible or have your vet complete the Veterinary Certificate (.doc).
In addition, you will also need a Third Country Certificate available from the EU Food Safety Department or the Norwegian Department of Agriculture.
Taking your dog to Norway from a non-EU country requires the dog (or cat) to be vaccinated for rabies, antibody-tested by an EU-approved lab, and be treated for tapeworm before traveling to Norway.
You must notify the Norwegian District Office about the time and place of arrival at least 48 hours prior (detailed information here).
When you arrive in Norway with your dog, follow the red 'Goods to Declare' line at customs. Norwegian customs personnel will help you with the process and will check the dog's (or cat's) papers.
Tip for booking your dog's flight: When you book your flights to Norway, don't forget to notify your airline that you wish to take your cat or dog to Norway with you. They will check for room and there will be a one-way charge. (If you wish to sedate your pet for the trip, ask whether the airline's animal transportation rules allow this.)
Please note that Norway renews animal import regulations annually. By the time you travel, there may be slight procedural changes for dogs. Always check for official updates before taking your dog to Norway.