Baby beef is veal.
Baby mutton is lamb.
Baby venison is ??
Is there a word for meat from an immature deer?
Looks like “baby venison” is just plain ol’ venison.
Is there a word for moose meat? I ate some on Christmas Eve.
It’s called “good”
Winklin.
Meat from a male moose specifically is bullwinklin.
Is there a word for moose meat?
Yes. The word is venison.
Illegal/immoral.
Most states specifically ban the killing of fawns. Only slob hunters will shoot a deer below a certain age/size. And why would you waste tag on a lesser amount of meat?
The hypothetical fawn in question may have been farm raised rather than hunted.
Ice Wolf, thanks for the link.
Eeewww! Veal is bad enough. Do you have a cite for this?
In Montana, we banned game farms but I don’t recall anyone selling baby elk/buffalo/deer meat.
I was sure this was going to be about porn.
Here in New Jersey it’s legal to slaughter hypothetical deer at any age. 
Sorry, no cite. Plenty of game farms online selling “young venison” which appears to be 1 to 2 years old, but none I can find selling the venison equivalent of veal. Not that that means it can’t or doesn’t happen…
I suppose if a hypothetical person was starving to death - in other words, in a true life-or-death survival situation - it might be ethical to slaughter a fawn and eat it. But most hunters aren’t that desparate.
That said, if the deer is farm-raised I don’t see it as being any more unethical to slaughter an immature deer than an adult. It may not make fiscal sense, though.
Many find veal objectionable not from the age of the calf but from what is done to the calf to maximize poundage per animal. In the “old days” - pre modern factory farming - veal was a thrify use of excess male calves and wasn’t any more cruel than any other butchering.