Having photographed pets my entire Professional Career, I have learned that the best images come from a little patience and a lot of fun.
Most of the time I still find myself using professional lighting mainly as studio strobes outdoors and in some cases indoors in family homes.

Just a little attention sounds (yes, I've been known to bark. LOL) to bring the pet's attention for a few quick simple portraits. 
Then it is to my editing to pop the images in the style that has become my own after all these years. 
This is where I usually state, "It's always about the people", well, it's also "Always about the pets.". 

Just have fun!