Here in MO, we can shoot does during any season. If I take one I take one right after the regular portion of firearms season. The longer you wait the more likely you'll be shooting a doe with a fawn inside. I don't like to shoot them during the rut (but I have before) because there may be a buck trailing behind them.
...and on that day when my strength is failing, the end draws near and my times has come, still my soul will sing Your praise unending, ten thousand years and then forevermore!