The old books I remember reading were prettty clear about how hunter-gatherer women were opportunistic small-game hunters (up to and including small deer.) Which makes total sense, when you're living hand-to-mouth like every other wild animal, you take what you can catch, because sometimes you catch nothing.

They also tended to be the ones to tend to snare lines.

Recent studies of savannah chimps (which is basically what "humans" started out as), suggest that spear use is more common amongst the females, precisely because they are weaker, and they generally use the spears to weaken small prey before killing it with their hands.