I assume she married in Australia, what details are given for her parents on her marriage.

Have you searched Trove for any details of her death as many death announcements in newspapers give details of where a person originated from. Also worth looking for her arrival in Australia, any ships lists all which might show more detail as to where she came from in Devon.

I think you need to do an extensive search of Australian records to see if you can find more details for her, especially where she originated from and her parents or siblings if they emigrated as well.

Even if a baptism is found for a Catherine Morgan in one of the many Devon Parishes without more detail it would be impossible to substantiate that record being for your Catherine's baptism.

You could try searching all Devon Parishes for a Catherine Morgan around 1812 remembering that a child is often not baptised shortly after birth. You could then work through any possible baptisms found and eliminate some of them by tracing that person's life.

Most Devon Parish Registers are available on Findmypast, not all have been indexed but all can be browsed. There are also 52 Parish Registers in the Members' Area of DFHS website, not on Findmypast, available to Members only and are not indexed yet. There are a few parishes where the incumbent did not give permission for their registers to be filmed so these will not be available anywhere online but might be available in BT's on FamilySearch. Again not all Devon BT's have been indexed on FamilySearch.

Have you looked at public trees on Ancestry to see if anyone else is researching Catherine who might have additional information about her that they are willing to share with you. Always check any information you find in a tree on Ancestry as details are not always correct or corroborated with documentation.

As you can see this is a mammoth task.