Time spent with animals is never wasted!!
I've written about the subject of photographing your animals before but it bears repeating. To see my first post on this subject click here. And I'll say it again, I couldn't create great portraits if I didn't have great reference photos! I know it's not easy but it's not impossible either...and can be a really fun time with your pet!!
You don't have to have special equipment but if you have a good camera, pull it out and dust it off! Never use your flash tho, instead get your pet outside in natural morning light. If that's not possible then in the brightest room you have.
Do your best to focus in on their eyes...get at or below their eye level. This adds an intimacy to your portrait and captures the soul of your sweet animal.
Also think about what it is that sets your pet apart from others...or what is unique to their personality. For my cat Shortie, when he sleeps or sees me he tilts his head a certain way.
And don't take just one photo and call it done...I can easily take 50 shots at one time, then whittle it down to 1 or 2 really great shots. Set up a few sessions to catch them in different moods. And above all be patient with both your pet and yourself.
Try these few tips and see if you just can't get that perfect shot off!!