Hi Anne Grant,
I cannot see a birth for Ernest BYE and Robert BYE, as brothers, however, there is every chance that they are brothers, and Robert's birth has not been transcribed, or registered.
I found this story about a Robert Roy BYE, born about 1903, a native of Mildura; who might be the brother of your grandfather, Ernest Murray BYE.
Marriage:
13383/1932 BYE ROBERT R ANDERSON HELENA REDFERN
Divorce, in April, 1943, The Truth, Sydney, 18 April 1943:
http://trove.nla.gov.au/ndp/del/article/168980886?searchTerm... bye" mildura&searchLimits=
If you purchased the 20.01.1955, death certificate of Ernest BYE's mother, Emily
GARBUTT/BYE, registered at Bourke, NSW, hopefully the children, are listed. However, her obituary, does not list a Robert BYE, as a child, but he may have been deceased by then, as Emily was aged 97 years.
http://trove.nla.gov.au/ndp/del/article/103934150?searchTerm... bye" mildura&searchLimits=
Mary