John Munday was a private marine in the 18th (Plymouth) Company who came to New South Wales on the First Fleet, bringing with him his wife Ann and son Edward.
John was a cloth worker from Berkeley, Gloucestershire, before joining the Marine Corps at Plymouth. It is uncertain which ship the family sailed on to New South Wales, suggestions being the Sirius or Alexander. At Port Jackson John served in the company of Captain Shea.
Ann Munday had a daughter Elizabeth at Port Jackson, baptised on 22 June 1788, followed by a son John baptised on 14 November 1790. Their eldest son Edward was born at Stonehouse, Plymouth and was probably a five year old when he made the voyage to NSW with his parents.

Artist Impression of Ann Munday with two of her children (Phillip Lock)
On 26 October 1791 the family sailed to Norfolk Island aboard Atlantic and there they farmed a 60 acre land grant. The fate of John and Ann Munday is not documented, both had disappeared from the records on Norfolk Island by 1805.
In 1802 son Edward Munday joined the NSW Corps at Norfolk Island, and in October 1805 departed Norfolk Island with his sister Elizabeth and the NSW Corps and their children aboard HMS Buffalo. In 1810 Edward transferred to the 73rd regiment and appears to have gone to Ceylon with the regiment in 1814. He was still on regimental pay records in December 1815, probably having seen action in Ceylon.
Previously on Norfolk Island, Elizabeth Munday had a child registered as Jonas Munday and a daughter Ann Wilson from her relationship with Peter Wilson. They departed the Island for Port Jackson in 1805 and were married at St Phillips Sydney on 1 February 1807. Also in the NSW Corps, Peter transferred to the 73rd regiment and left the colony for Ceylon in April 1814 aboard the Wyndham. It is presumed Elizabeth and their children accompanied him.
John Munday jnr settled in Van Diemen’s Land around 1818 and held land at Kangaroo Point. It thought Edward joined him at Clarence Plains around 1826 having spent many years in the Army. Edward Munday was aged 48, when he was buried on 4 May 1832 at Clarence Plains.
Reference:
Gillen, Mollie, The Founders of Australia, A Biographical Dictionary of the First Fleet
Holden, Robert Orphans of History, The Forgotten Children of The First Fleet
The Eureka Times Quarterly newsletter of the Eureka Council Inc (NSW), Autumn 2007