I notice one of the daughters of Robert & Emily had the 2nd given name Joyce.
Coincidence???
The 1936 burial of Robert BYE is listed here:
http://www.bencemtrust.com.au/deceased-search/I think as others here have suggested you might be best to order one of the birth certificates of Robert & Emily's children. Australian certificates are very detailed.
You can download a pdf image of a certificate at quite a reasonable cost at
https://online.justice.vic.gov.au/bdm/index-search?action=pu...Only once you have done so will you know for sure if this is the right Robert to follow.