This is a tricky one, so watch out. Charlotte Smith was writing during a time when very few women wrote professionally (the late 1700s), and those that did were often criticized for making a profit by writing about their feelings (gasp!), which people argued should be kept private. Charlotte Smith was very sensitive to this kind of criticism (check out the link to the Preface she wrote in "Best of the Web"), and you can see evidence of this sensitivity in most of her poems, including "To Melancholy."
What lady poet? Charlotte Smith tries to remain sexless in "To Melancholy" in order to assert herself as a "poet," not as a "lady poet." Her gender, she suggests, should not matter.
Charlotte who? Autumn, which is personified as a woman wearing a "veil," is a kind of stand-in for Charlotte Smith herself, who felt the need to "veil" herself in a world dominated by male writers and publishers.