If you have the opportunity, it's best to take some photos with the needs of a portrait specially in mind. For some animals a good photograph representing your pet's best qualities is very easy, for others it is more elusive.
Some people choose to have professional photos taken.
While this can be a good solution, with a little preparation and patience you should still be able to achieve similar results yourself. Try to do this even if your pet is an indoor only pet avoid direct sunlight, as this can alter natural colouring. This can also cause red-eye. Don't have your pet looking up at you unless this is how you want the portrait to appear. Don't make them come to you.