She took ship for Canada, met up with a dashing con man, ran away to the States to escape creditors, ......

Seriously, the chances of finding public documents that would answer such a question are slim.

An obituary may contain such details.

You have to work on the balance of probabilities.

The family quoted above in the 1871 census does not appear to be in the 1881 census for the Island.
Of course, Louisa may have married by then and be there under a different name.
I don't see any burials for the parents.