Eeee! You get to be among today's lucky 10,000! This is so COOL!
So it turns out that antlered does are actually not that uncommon in whitetail deer. My guess--and this is only a guess--is that they're probably found in a lot of species where the males have antlers and the females mostly don't,* we're just particularly aware of it in whitetails because they're a super-common game animal in the US AND hunters in most areas are only supposed to take bucks,** so you get a good amount of reporting on the subject when a hunter drags in a deer and says "Look, I saw antlers, but this is NOT a buck!" (So far as I know the DNR does not yell at anyone about accidentally taking a doe when it's obviously got a rack of antlers on it--it's the definition of an honest mistake.) The DNR says that it also happens in mule deer and blacktail deer, anyhow.
You find variable numbers on this, but based on the deer herd culls and the hunting records, the Minnesota DNR think you get about one antlered doe per 1,000-6,000 whitetail does. Apparently there was a study in Alberta, Canada, that had a population throwing an antlered doe at a rate of about 1 per 64 does, which is much higher than anyone expected, but I don't know any of the details.
Most of the time, these aren't very impressive antlers--they're just spikes, like you get in young bucks--and they're caused by a biologically female deer having a testosterone spike, for all the various reasons that can happen, which are as varied in deer as they are in humans. One source claimed that in a biologically female deer, the antlers generally won't go out of velvet (apparently that requires a second hormone spike) but here we are getting beyond the limits of what I can say authoritatively about deer biology. Either way, most of those does don't have very big racks, and the ones that do tend to have very weird racks--they'll be asymmetric and they'll keep growing in weird shapes or whatever, so you can get thirty-point does because they never get the hormone surge that shuts off growth.
(Weird antlers happen in biologically male deer too, of course--any time you get a process that complicated, things occasionally go haywire.)
Some deer, however--another source estimated 1 in 20,000 does--are either true hermaphrodites or "pseudo-hermaphrodites," in this case having female external genitalia and male internal organs, and these deer will grow a full-on rack of polished antlers that lose velvet and everything and which are often not distinguishable from a standard whitetail rack.
As with anything involving sex organs, there does seem to be an enormous range--I've always found antlered does fascinating and have been reading about them for years, so I've read cases where you'll get does that have a rack and fawns at the same time, does with antlers that mount other does and even keep and defend harems. There's some minor sexual dimorphism in whitetails around the head and neck, and you get antlered does on both sides of that spectrum. There is a LOT of variation.
At any rate, other than the minor inconvenience of having to burn calcium growing antlers, none of this seems particularly detrimental to the does. Hunters usually describe them as being perfectly healthy when taken, and in the majority, they're still breeding successfully, so it's just one of those nifty things that happens in nature sometimes.
Anyway, that's antlered does! Isn't that cool?
(Someday I will do something with the antlered doe character I had kicking around in my head for years, but I'm still not sure how her story should go...)
*Actually, I suspect this sort of thing happens with most species, it's just that when you've got a really clear marker like antlers, AND in a species that has a major economic impact, people actually notice and study it.
**I have Very Strong Feelings about this from an environmental perspective, but that's another topic and today we're talking about a REALLY COOL THING! so we won't spoil it.
Article where most of those figures came from