OK, here they are in 1861
28 Brech Road, Everton, Liverpool
James Gilbert Howson, head, b. abt. 1832 Newcastle, Staffordshire. Foreign Trust Merchant
Elizabeth Brooks Smith Howson, wife, b. abt. 1833 Liverpool
Henry Brooks Howson, son, b. abt. 1859, Everton
Lizzie Hardley Howson, daur, b. abt. 1860, Everton (age 7 months)
Elizabeth Coghlan, servant, b. abt. 1840, Ireland
James' job sounds quite important, perhaps that is what took them overseas.
I have looked for an immigration record for young Lizzie but can't see her. The immigration records I posted above were individual so there may have been others travelling with them.
Jool