It's cool

It actually sounds to me like you'd be better off not covering the spa. The cover would be costly and you risk marring the deck when the anchors are installed. As long as your dog won't go in without a cover on it, let it ride - it's a little more work on your part to keep the spa clean, but you can get a decent leaf-rake for $15 - 30, to get the large debris and then just give a good vacuum when you want to use the spa again

I'm not sure if you winterize the spa but, either way, I think you'll do OK without a cover.