The site of the State Library of Tasmania briefly presents the O’May shipping company:
“Robert O'May (...) with his brothers, Thomas and James founded the Hobart-Bellerive ferry service. (...) In 1912 the O'May Brothers who owned and operated the trans-Derwent ferries merged with the Rosny Estates Company to encourage property development on the Eastern Shore. The venture failed and the company folded but the O'Mays continued their ferry service. However it became largely redundant when the floating arch bridge (in Hobart) was opened in 1943.”
O'May operations started, I believe, in 1870.
A small house flag (part of a display set, not an original) is presented here (image clickable). Described as “red with a black and white centre”, this really means a red field bearing, in the centre, a disk horizontally divided white above black.
Pre-1912 (before merger)
More pictures from SLT show a disk divided white above blue, such as found in a 1910 Christmas card. This and similar pictures originated before 1912 showing a conjectural O’May house flag preceding the 1912 merger.
O'May Brothers, Ferry operators in Hobart from 1863 with a red flag having a white circle divided horizontally white over blue as shown by The Log 2/1991. The actual flag as displayed by the State Library of Tasmania site has the circle slightly smaller and appears to show the circle as white and black. However a close look at the photo appears to show blue tints suggesting that the black is actually a dark blue. In 1912 the brothers merged into the Rosny Estates & Ferry Co. retaining the flag. The company went into liquidation in 1926 but in 1927 it was restructured as O'May Bros. Pty. Ltd. and continued trading until 1939 when the Tasmanian Government legislated that the Hobart Bridge Co. Ltd. have sole rights to transport across the Derwent River.