This is from Sports and Pastimes of England, published in 1801. It seems ladies were not only allowed to practice hawking, but some may have been rather good at it:
Ladies not only accompanied the gentlemen in pursuit of this diversion, but often practiced it themselves; and, if we may believe a contemporary writer, in the 13th century, they even excelled the men in knowledge and exercise of the art of falconry, which reason, he very ungallantly produces, in proof that the pastime was frivolous and effeminate. Hawking was forbidden to the clergy by the canons of the church; but the prohibition was by no means sufficient to retrain them from the pursuit of this favourite and fashionable amusement. ON which account, as well las for hunting, they were severely lashed by the poets and moralists; and, indeed, the one was rarely spoken of without the other being included; for those who delighted in talking were generally proficients in hunting also.