To follow in father's footsteps is a cliché which means to take up the same trade or pastime as one's father, something that is very common in music and the arts generally.
A song with this title was written by E.W. Rogers and published by Francis, Day & Hunter of London, copyright 1902. It was sung by Vesta Tilley, and might be classified as a novelty song because Vesta Tilley was the pre-eminent male impersonator of her day. Though English by birth, she was equally well known on both sides of the Atlantic.
Vesta recorded her song on Edison Gold Moulded Record, c1906, a copy of this is held by the University Of California Santa Barbara Cylinder Preservation And Digitization Project (as "I'm Following In Father's Footsteps").
Alexander Baron - London, England