The Ayrshire school will meet the winners of the tie between Glasgow High and Stonehaven High in the third round, which is scheduled to be completed by October 22.
Edinburgh's George Watson's College have also received a bye to round three, where they will face the winners of the second round tie between Royal High and Waid Academy.
Eight schools are involved in this month's first round ties (St Margaret's School, Edinburgh; Robert Gordon's College, Aberdeen; Albyn School, Aberdeen; Nairn Academy, Highland; Glenalmond College, Perthhire; Grove Academy, Dundee; Cults Academy, Aberdeen and Balwearie High, Fife) and a total of 36 schools have entered the girls' event.
There are 37 teams in the boys' cup, 10 of which are involved in this month's first round (Lomond School, Helensburgh; Jordanhill School, Glasgow; Cleveden Secondary, Glasgow; Lanark Grammar, South Lanarkshire; Belmont House School, East Lothian; Stonelaw High, South Lanarkshire; Hermitage Academy, Argyll and Bute; High School of Glasgow, James Young High, West Lothian and the Royal High, Edinburgh).
The first three rounds must all be played by October, with the latter stages being staged next June and the final on June 21.