Cloudy Day = Great Lighting
For the most detailed and balanced portrait, consider using Diffused Light; which is best known as a Cloudy Day! A layer of clouds scatters the suns direct rays into a soft, even spread that allows you to see all or most of your pet without creating harsh shadows. This type of lighting is perfect for closeup portraits.
Dramatic Interior Lighting
Pose your pet near a window in the morning or evening when the light is sweeping across their fur to create a dramatic, or soft and calming portrait. Dappled light from the shadow of leaves or curtains can help soften harsh light.
Tell A Story With Setting
Does your dog wait in the same place before going on a walk? Or do they always curl up in the same place to catch a patch of sunlight? Look for a combination of that special place, along with good natural lighting, (especially morning and early evening around sunset) to pose your pet that brings a part of their personality or behavior into the portrait.
Raking Light
Near sunrise and sunset, sunlight creates light shafts that cut through the window, and can create striking and dramatic portraits. When posed near a window in direct light, the light can "sculpt" the form of your pet, or can catch on long patches of fur in a dazzling glow. This works best against a darker background, but these types of photos can be challenging to use because the dramatic lights and darks often cause difficulty in showing detail, but as a tradeoff, they are exellent for creating mood and a dramatic pose.