Was David's wife Jane's maiden name also Robertson?
At this point I just don't know
Ah.
In Scotland, a married woman does not legally lose her maiden name on marriage. The result is that she tends to be listed using her maiden surname in older records, and deaths of married women are indexed by both maiden and married surnames.
So what we know is that James Robertson and his wife Jane (who might also be recorded as Jean) had a child in Tasmania in 1832. (It seems unlikely that the James Robertson who arrived in Tasmania on 30 September would be the father of a child born in Tasmania earlier the same month, surely?)
James could not have married before he was 14, and he is unlikely to have married before age 20, and he had left Scotland by 1832. The index at Scotland's People lists 21 marriages of a James Robertson to a Jane, and 42 to a Jean, between 1820 and 1832.
If you are prepared to spend a bit of time on this, there is a way to narrow down the possibles.
Go to
https://familysearch.org/search/collection/igi and search for children born to James Robertson and Jane between 1832 and 1854. Then compare the mothers' surnames to the list of Janes and Jeans from the SP marriages, and cross off any who were having family in Scotland in the 1830s and 1840s. This will leave you with a list of James Robertsons who married a Jane/Jean and were not having family after your James and Jane left Scotland.
This is not a perfect solution because (a) not all marriages are in the records (b) for completeness you would have to do the same exercise using the Roman Catholic and Other Churches sections of the SP web site (c) there could be couples who had no children or who also emigrated before 1832 (d) I am sure there will be other reasons I have not thought of. Whetever you do, it is never safe to assume that, just because there is only one possible candidate in the records, it has to be the right one. We have all made that mistake and spent time climbing the branches of a tree that isn't ours!
As an example, a James Robertson married a Jane Brodie in Perth in 1826. This couple had a son James, born 1830 in Perth, but no more children are listed. So this couple could have emigrated and had more children in Tasmania. (Did your David have an elder brother James, I wonder?)
On the other hand, James Robertson and Jean Mowbray, married in Edinburgh in 1827, had a daughter in Edinburgh on 4 June 1832, so you can safely cross this couple off the list of ones who might have been the parents of your David.