Hi Erica,
Welcome to the Forum.
The earliest reference to the company that I can find is this advertisement from January 1987:

Whitehill Silver and Plate Company - Melbourne - 1987
Your mark image shows that the company may well have used a date letter system at one time:
But it appears perhaps now abandoned:
This is presuming that the two different styles of marking belong to the same company, or maybe even the revival of a defunct company?
How did you come to the conclusion the the letter 'Q' relates to 1958?
Trev.