The photo is nice Diane. I would suggest that you invest in some muslin backdrops, blankets, or table cloths to use as a background. You don't need to invest in a lot of equipment. A backdrop stand, a couple of backdrops, and if you are going for the studio look, some strobes.

I do what you are starting to. I go to peoples' homes and take portraits of their dogs and cats. If you don't have room to set up the stands, just throw the backdrop over a couch, chair, etc. I found a bed works great, throw the backdrop over the headboard, or even set the backdrop stands on either side of the bed.

Lots of luck, your photos are nice.