There is a possible entry into the US from Canada in October 1923 by this group:
Isabella Taylor, married, 43 b. Alloa
Jeannie (hard to read) Taylor 14 b. Glasgow
Mabel Taylor, 12 b. Gourock
They are joining father/husband John Taylor in Newark, N.J.
Can't easily see a marriage for a John Taylor and an Isabella
Campbell on the official pay to view site
www.scotlandspeople.gov.uk There are also no births showing with the middle name of Blackburn which would help narrow down the options.
One thing that might help is the imminent release of the Scottish 1911 census on 5 April this year. Bare in mind when searching for Janet that this name often has variants (Jessie, Jean(nie) Jane are some common variants).
Have you tried searching for a marriage or death registration for Janet to confirm parents' names this way?
Monica
