Of course a woman can do it! I'm 63, and still dig out huge established roses by myself. You don't have to get all the roots out; just get as much as you can. And, yes, you can re-plant a rose there, if you take precautions. These include: removing as many of the old roots as possible and then,re-digging the area,adding oodles of organic matter and other goodies (I use expanded clay and betonite-based kitty litter and potting soil),and also at least one wheel-barrow-full of native soil, taken from a place in which roses have never been grown. If you want to be extra-careful, wait a year before planting the new rose, and sow marigolds in the area; if grown from seed they are said to help.