For pet portraits I work from photographs, either taken by myself if local to North West, or by the client. For a portrait to be successful these photographs need to be as clear as possible and this can be a challenge.
Reference photographs can be taken either inside or outside, and there is no need to worry about the background as the focus will be the pet and anything else will not appear in the portrait. I can artistically insert suggestions of natural backgrounds.
Take and send as many photographs as you can, it is always better to have too many. Try to fill the frame with your pet to give me the maximum detail possible. Also avoid bright days or unnaturally bright lighting, particularly if your pet is light in colour. Head portraits similar to the example above work well, but you may prefer full body. Which ever you choose, a modern camera phone is more than up to the task.