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.