With just my wife and myself, I try to target fawns in late December. My reasoning is your are doing exactly what most predators key in on, young, weak, or sick. I figure if I shot an adult doe the fawn she carries is dead as well, a net 2 deer loss, maybe more if a area has few deer to begin with. Harvesting an fawn in the late fall is a net zero loss, as the fawn is replaced in the spring.
I have harvested 2 fawns from one doe over the past 3 yrs both fawns fell within 20 ft of one another.
My .02