The logo should be pretty clean, simple, and friendly. It must scale well - very small for a Facebook thumbnail, but also large for website and t-shirts, etc.
Please avoid very cliche elements like a dog with wings and a halo playing a harp. Also no overly-cute cartoonish animals. Animals are fine, but they should be drawn with a respectful, sincere tone.
The slogan is: "Gone but always with us". Feel free to include that in the design, but it's not necessary.
The demographics: middle-America, skewing female, down-to-earth pet lovers, traditionalist, sensitive.
The psychographics: people who have recently lost a pet, so they're sad, in need of support and connecting with other people to help them feel better.