If your father was born in England, it should be pretty easy to find a copy of his birth certificate.
You know his name and his date of birth - right? If you know your grandparent Dowleys' details you can start with them. (Are you in the UK or Oz?)
Family Records Centre in London or a big public library, or a Mormon Family History Center, will have copies of the Indexes to Births, Deaths and Marriages. I can explain how to access the details and get a certificate, if you want. It only costs a bit of time and £6.50 to order it up. Dowley is a rare name which oddly makes it easy to search for!
The birth certificate will give details of the parents and enable you to search further back in time.
I happen to have Dowley relations currently in Australia and Liverpool, but I think just a coincidence as they only moved there after WW2.
My Dowley family are from the London area, and go back there at least to 1780s.
Another Dowley group were in Derbyshire in the 1600s. Some Dowley researchers think a son of this group may have moved to London.
The name DOOLEY (sometimes spelt DOWLEY, but pronounced DOOLEY) would indicate a separate family from mine and an Irish origin. (It is just possible this might explain your link with Liverpool.)