Have you found the birth record for Rose Ann in Scotland on Scotlandspeople?

I did find the following passenger record:

Aboard the Webster out of Liverpool arrived in New York on September 3, 1855:

Murphy, Michael, aged 27, laborer, born Ireland, bound for Illinois
Murphy, Margaret, aged 26, servant, born Ireland
Murphy, Mary, aged 24, servant, born Ireland
Murphy, Rosey, infant, aged 6 months, born Scotland

Mary may be a sister to Michael, and that would mean that baby Frank was likely born on the ship (altho' no note appears) or in Illinois. This also makes Michael a couple of years older than you think.