I have encountered a slight issue with designing pets. If you are designing a pet specially for someone else, you don't necessarily want it to be public.
Maybe set it up the same way as selling and breeding but without a fee.

if you don't want people to see your saved design, you can save it as a private one; and if you're willing to show it to the person who you've made the design for, you can send the image in a private message.