The draw for the first two rounds was shown on Notts TV on Thursday evening.
Eighteen teams have entered, although one has withdrawn since (not sure who). So we have just two games in the first round followed by eight in Round Two.
The draw is as follows...

Notts FA Women's County Cup : Round One

(Match 1) Nottingham Trent University 2nd XI Women v Mansfield Hosiery Mills Women
(Match 2) Arnold Eagles Women Flyers v Bingham Town Women

Round Two

Nottingham Trent University 1st XI Women v Bye
Arnold Town Ladies v Teversal FC Ladies
Retford FC Women v Notts County Women
Mansfield Town Ladies v West Bridgford Colts Women
Arnold Eagles Women v Winner of Match 1
Keyworth United Ladies v Nottingham Forest Women
Sherwood FC Women v Winner of Match 2
Rise Park Ladies v Gedling Southbank Ladies

Dates of the matches is still to be confirmed.