Thanks for the info. My own GGF was b in Kilmarnock, and then moved to Glasgow as a young man where he married. My GF later moved to Canada and brought out his young family. It looks like you have taken to OZ, and I'm impressed by the photos and work you have done in tracing your roots.
I found Jean Duffy in her Kilmarnock family in the 1901 Census but nothing since. She was then age 12, which means she was b 1889 (approx.) and 18 when Lizzie was born.
It is quite possible that she and David Dorans were out of Scotland a short time for the 1911 Census, as they don't appear to have emigrated (v. the 1925 Wedding!). The
relatives who emigrated earlier to the States were the family of an earlier David Dorans (possibly an uncle) and they left Scotland after the 1881 Census. His daughter Agnes married Thomas O'Brien in TORONTO, OHIO in 1888.
I'll just keep looking for additional leads, and await any further input you will have.