There is an on-line tree with information about a William BEER who is shown as marrying Hannah McDonald as you've already said.
The information on this tree regarding the origin and arrival of William BEER is almost certainly incorrect. This is not your man - see below
There is this arrival shown from the New South Wales, Australia, Assisted Immigrant Passenger Lists, 1828-1896 (The image for this man is shown as "Married Immigrant" so it's unclear fi he's the same person as your William.)
William BEER arr per Marquis of Hastings, arr February, 1841
Brought out by C F Warne?
Native of parish of St George, Exeter
Parents: John and Elizabeth, living at Ditsam, Devon
Calling: joiner
Age: 24 on 4 January, 1841
Persons certifying character: Thomas Lamerton, William Main/e
In good health; religion Church of England; can read and write
His wife on the voyage:
Mary Jane BEER, nee Lamerton
Native of parish of St George, Exeter
Parents: Father Thomas Lamerton, Guinea St, parish St George Exeter
Calling: uphosteress
in good health; can read and write
Age 25 on 28 April 1840
However, when this Mary Jane BEER dies in 1857 she is described as wife of William BEER, and has children to him up to 1850 so this is not the correct William BEER. However I'll leave the information here as it may help someone else
Judith