RootsChat.Com

Sarah and Francis married 13 Sept 1819, and less than a year later he was dead (hanged on 18 Aug 1820). We will never know if Sarah was pregnant with Mary Ann when he was executed, or if the child had already been born.

Also Maryann daughter of Sarah McElroy and Mathew had McGowran at the end of her name.
Janet

Since Sarah and Francis were married in 1919 it is most probable that they had a child a year later. This may have been Mary Ann, but there is no record to confirm this. Mary Ann may not have known who her real father was, or did not use his name on purpose. There would have been a great amount of family shame being connected with a convict who had been hung to death. The father who brought her up (if not her biological one) was Mathew McIlroy.

I think you are getting your self confused without reason. Do you have original documents of marriages, deaths, births, and Francis's trial, etc?
 What is all the information that these documents give? I am not on Ancestry at the moment, so I can't see what you are looking at.
I would also ignore the web site that you found relating to Mathew mcIlroy and Sarah - it is perfectly possible that not all information there is correct.

In wiki, it is incorrect and he is listed as "Thomas" McGowran. This is because whoever wrote the wiki entry, did not do enough research, and took their information from one newspaper report where Francis is called "Thomas" by mistake. Newspaper reporters got things wrong, even in those days. All the correct information is available from the NSW State Archives -  This is the link.
https://search.records.nsw.gov.au/primo-explore/fulldisplay?docid=INDEX93216&context=L&vid=61SRA&lang=en_US&search_scope=Everything&adaptor=Local%20Search%20Engine&tab=default_tab&query=any,contains,francis%20mcGowran&offset=0

Maritime medal here
https://discovery.nationalarchives.gov.uk/details/r/D6769195