Baking shaped cakes is in the tradition of the "Gebildbrot" (image-y bread; link takes you to German Wikipedia, which has some images), and that reaches back a bit. It also seems to be a German-Austrian thing, though specially shaped baked goods do occur in other countries.
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If you eat the antlers first, it looks much more lamb-like...
We have the Easter bunnies and lambs, though. There's also yeast dough bunnies and lambs. Plus, in the wintertime, there are gingerbread men, and other gingerbread shapes. There's the Stollen, too, which is supposed to remind, with its form and white sugar covering, of the swaddled child. And even the very common find-it-at-every-bakery-every-day pretzel is a form of Gebildbrot. Then there's the Plätzchen, with their many shapes and forms, that get baked for Christmas (and, to a lesser extent, for Easter).
Anyways... back to the lamb. Traditionally, the way I know it and grew up with, the cake made in lamb-shape is a very simple one, nothing fancy: flour, eggs, sugar, baking powder, a bit of lemon peel grated in and maybe a dash of lemon juice. That's also the kind you would get at a bakery. When I was small, our church also gave out a lamb as a present to each of the helpers with the festive service. (Everyone who attended got an egg, coloured, of course, that had been blessed.)
The moulds are usually considerably smaller than normal cake tins, so my mum always made additional small cakes to use up the batter. The cake she made in the bunny mould was usually a marble cake, one of the usual suspects to be made in our home (with lots of dark and little light dough, because everyone liked it better that way). I made an eggnogg cake for the elk, because of eggnogg being there, and anything with eggs is considered quite easterly, so it sort of fit. (Delicious, too, by the way.)
Baking in these shaped moulds is quite fun, but you do need to grease them thoroughly and then powder them with crumbs, or ground nuts if you like nuts, so the cake will not stick. My elk has an anti-stick coating, which does help, but it still needs the assistance. The older bunny mould my mum has really, really needs the buttering and crumb-coating, else you'll have bunny crumbs only. Also I tend to fill in too much dough, and there's always some left over anyways, which means it's a good idea to have an extra small cake tin or some muffin thingies handy. Unless you like to eat lots of raw cake batter, of course...