I've seen sharks as the premium item. I don't see why golden stags wouldn't have a chance to be premium.
I'm not sure if I'm correct on this or not, but I've noticed that ReTail's premium item is limited to what fish and insects can be available in your town for that season. Stuff like non-native perfect fruits and things like that don't count, it's only for fish and insects. For example during the winter, I kept seeing stuff like the mole cricket and pillbug go on premium (so useful!), but I never saw any of the profitable beetles or sharks. So even though you can go to the island where it's summer and catch golden stags, you may not be able to sell it as a premium item if your town is in winter/fall/spring.