You make gingerbread animals just like gingerbread men. Use the recipe on that page of this site OR any of the gingerbread house recipes if you prefer. Once you have the dough rolled out flat, use animal cookie cutters to form animal gingerbread cookies. If you don't have any, try cutting out your own animal shapes. Or search the web for "animal clipart" and you're sure to find simple designs you can print, cut, and use as templates for your animal cookies.
Send us a picture when you're finished so we can see how they turned out!
I'm currently working on gingerbread house templates for this site. We had 1 request last year for 3-D gingerbread reindeer (as shown at the top of this page.) I'll see if I can make a template for that as well. If you're interested in any other animal gingerbread templates, comment here and I'll attempt it.