I am not so concerned about the WALSH family starting out in Bathurst. But a child then born in Sydney, and the family contunuing to regional Victoria makes the Sydney visit look odd.
What names do you see for witnesses at the 1867 marriage, James WALSH?
Usually, when a BDM event is recorded in one state, and references a location in another state, the record shows the name of the state eg Bathurst NSW, Sydney NSW. So Bath seems a bit odd. Also Sydney , with no state.
Are you looking at a handwritten document or is it a transcription?
Where is the death record in the VIC BDM index for Mary Ann WALSH,5 deceased at 1867?
Does it mean that Mary Ann would have been five in 1867, or did she die at age 5?
There should be a death to find for Mary Ann WALSH/WALCH/WELSH in Victoria, died 1860-1867?