Hyperrealism Paintings require high resolution images as shown in example #1 that are in focus and detailed. If we can see it we can recreate it and bring out unseen beauty. We can only recreate details we can see and some images can not be used for a hyperrealism painting based on quality. If you do not have a high resolution image of your pet, then it is likely that we can only produce a more playful style painting as seen in example #2
If the playful painting style is what you are looking for, a high resolution image is perfect for that as well.
The Eyes - As long as we can see the true color and some detail of the eye.
Nose and Mouth - A little blur on the nose is fine as long as the true shape and color can be seen. If the mouth is open we need it to be clear in order to create higher detail but not absolutely necessary.
Hair/Fur - A little blur in the hair is ok as long as we can still see the detail of the hair in most of the image especially in the face. The face is most important so please make sure the details can be seen.