Can you do a give away in a group?

I was wondering if you are allowed to do giveaways (prizes) in groups?

Here is my thought...

I know that when I eat healthy and exercise it directly affects my dog. I have more energy, I take her on more trips hiking, and so on. So I was thinking, wouldn't it be fun to start a group where the winner could earn a prize to benefit their dog. I own a small business here in Maine and I make dog toys and leashes out of lobster fishing rope (new rope for safety of the dog). I was thinking on doing it on the honor system, highest % weight loss wins and gets a dog toy for their pet. They don't pay shipping or anything.

I know you can't advertise your business on here because of rule "#14 no advertising, self-promotion, or fund-raising" but if I don't say the name of my business or list my website can I give out a prize?