To keep your followers engaged, post anywhere from everyday to a few times a week.
In order to take excellent shots of your pet, you need to find your pet's good angles, decide what time of day is best for taking photos, and download apps such as VSCO and Snapseed to edit them.
Use appropriate hashtags in order to get your photos noticed by other users. Some hashtags that work for pets are #cute, #doggos, #tongueouttuesday, #fuzzy, etc.
Once you find that special something about your pet, use it to your advantage, and start working on creating a signature look or style for your pet.