Goodall was born in 1822, the second son of steel line engraver Edward Goodall (1795–1870). He received his education at the Wellington Road Academy.
Frederick's first commission, for Isambard Brunel, was six watercolour paintings of the Rotherhithe Tunnel. Four of these were exhibited at the Royal Academy when Frederick was 16. His first oil won a Society of Arts silver medal. He exhibited work at the Royal Academy 27 times between 1838 and 1859. He was elected Associate of the Royal Academy in 1852.