Welcome Webster,
RootsChat is a great place for help with family history.
If you are based in New South Wales, and can get to the NSW State Library, their holdings include excellent resources re the 73rd Regiment.
From my resources I can confirm that there was indeed a Matthew KELLY of that regiment :
December 1809 NSW General Muster.
Matthew KELLY, Private 73rd Regiment, in the following companies 9, then 4, then 8
Arrived NSW as part of the garrison force for penal settlement …. Arriving per Dromedary or Hindostan 28 December 1809.
Departed per Earl Spencer 25 January 1814 for Ceylon.
There are many NSW resources for Penal era, particularly the Macquarie decade. Here's a live link to the NSW Col. Secretary's papers 1788-1825.
http://colsec.records.nsw.gov.au/ So, check under "Seventy-third Regiment" and their officers for additional information.
There's also a free to search index that is becoming quite popular as it gathers more and more information and databases. Biographical Database of Australia .... there's a nominal annual subscription for access to the full database, but the index is freely available.
Under their sources are many headings. Free to search

on heading is "Military" and under there, again, free to search .... 73rd Regiment on Foot .... eight pages of quality info.
http://www.bda-online.org.au/JM