I have done a quick check on the Free Surname Search facilities of Scotland's People, rhe most comprehensive site for Scottish BMD and other records-
Census 1861.Learn more. 4 matches
Old Parish Records Births & Christenings 1538 - 1854.Learn more. 4 matches Old Parish Records Banns & Marriages 1538 - 1854.Learn more. No exact matches Old Parish Records Deaths & Burials 1538 - 1854.Learn more. 1 match
There are 22 Record Sets total, all of the others are "No exact matches".
Census 1871.Learn more. 15 matches
Old Parish Records Births & Christenings 1538 - 1854.Learn more. 1 match
Old Parish Records Deaths & Burials 1538 - 1854.Learn more. 1 match Catholic Parish Records Births & Baptisms 1703 - 1992.Learn more. 2 matches
Not unexpectedly, there are many results to this search.
With the Battle of Culloden taking place in 1746, the later Census results above are very unlikely to have any connection.
Regarding the name change from McRae to Glasgo, I suggest that you should be wary of this for the following reasons-
a) If Charles did this in a region where he was already known as Charles McRae, this would simply draw attention to himself, particularly retaining his First Name. (That retention might be explained as being that he would respond almost inately to "Charles" or related diminutives such as "Charlie".)
b) If he made the change in Ireland, why choose a name which would very solidly connect him back to Scotland?
c) More generally, last year I read the "Act of Proscription" passed very shortly after that Battle and the Second Jacobite Rebellion. It does NOT proscribe (ban) any names or clans at all.
Checking the alleged "banned" name involved, there was a slight decrease in the Births recorded in 1745 and 1745, which could probably be explained by the absence of the men-folk following Prince Charles down into the Scottish Lowlands and onwards as far south as Derby in England, with substantial periods camped in specific towns, followed by the retreat northwards culminating at Culloden Moor.
There then followed increases of the recorded Births of the allegedly banne surname, to a level HIGHER than the years immediately prior to 1745.
Hardly what woould be expected if the name had been banned.
The ban was on "Highland dress" and the bagpipes; and the Act was abandoned surprisingly quickly.
If you go to the LDS Family Search site, there are about 150 Glasgo Births in Ireland (and there could be many more - but the records are not available on line).
The earliest of those LDS FS Glasgo Births is 1809.
There are six GlasgoE Births, all 19th century.
There appears to be over 200 GlasgoW Births, checking about half,, again these are 19th century.
As the 1840 Australian Arrival looks more solid, you should first try to confirm that in the Australian Archives, whether directly in Arrivals Lists (Very good in my limited experience of them); and also for subsequent events such as the Birth/s of more children, Deaths etc.
The more solid your information from reliable Australian Archives, the better.
Remeber to note your Sources and include them in any posts that you make.