There is an Ann SHARKEY with correspondence in the Col Secretary Papers index, noting she came per the Friendship, and was in the Liverpool district and seeking permission to marry there in July/August 1818, and I think she may be your lass… http://colsec.records.nsw.gov.au/ ......
So that is for a request made in July 1818, and it was lodged by one of the Assistant NSW Chaplains and it was approved by Lachlan Macquarie, NSW Governor. So the administrative officers of the NSW Colonial Secretary's Office had to go back through their records to check and so from an historical perspective, whether Ann arrived per Canada (4) or Friendship (2) is of little consequence, BUT ... we do need to recognise that the Permission to Marry record does show that Ann arrived per the ship Friendship and makes no mention of the ship Canada. Both those ships transported female convicts to NSW, Canada in 1817 and Friendship in 1818. Under Macquarie, the administration became focused on documenting just about 'everything' including many clerical aspects that follow the same 'rules' developed by Macquarie even now, in the 21st Century here in NSW.
If I were asked to consider if info on a Muster Roll was more reliable than info on an Application to Marry, I would say
'cannot give 100% assurance, but I think Application to Marry would be more reliable, particularly if it was given within a reasonable time frame after arrival.' I note that Ancestry has a current partnership with NSW Archives.
1823 Liverpool (NSW) population Book,
Ann SHIRKEY, FbS (Free by Servitude) Canada 1817, 7 (years), Wife to Wm Herbert
Marg SHIRKEY, 4, BC (born in the Colony)
Wm SHIRKEY, 1 BC
1822 General Muster
Ann SHIRKEY, C (Convict) Canada, Wife of Wm Herbert
.. SHIRKEY, 3 BC
SHIRKEY, 2m (2 months?) BC
I have NOT located any Muster Roll or similar for NSW for 1818
ADD, my reasoning would be that it would be a separate action to check the documents for each Application to marry and then to have these signed off, whereas the Muster Rolls would become a mundane checking task and thus easier for slip of pencil. So if in 1823 you were to check back, you would likely only check back to the most handy - ie the 1822 roll and not go back to first principles each time, whereas with marriage, as a clerk, checking an application, you would be aware of the religious importance of the ceremony... afterall, you too were required to attend church every week as per Macquarie's regulations, and if you did not, then you ran the risk of being charged, and transported to .... Newcastle or further.
JM