Hi Brian.
Welcome to this wonderful site!
The Public Records Office of Victoria (PROV) has just made access to passenger lists available online so you might find some information there:
https://prov.vic.gov.au/If your GGGF was born in Buninyong then there should be a record available on the Victorian Births Deaths and Marriages site ($20 per record, and they arrive in the email within 5 minutes) here:
https://www.bdm.vic.gov.au/research-and-family-history/search-your-family-historyIf he was in Buninyong then it's likely that he was a gold miner. I have found the Linton Historical Society very helpful:
https://www.lintonhistory.org.au/Ballarat Historical Society might also be helpful:
http://www.ballarathistoricalsociety.com/My GGF was a Durham coal miner who came out in 1861 and he worked at Happy Valley, which is a few kilometres south of Buninyong and east of Linton. There was a big mine at the town of Piggoreet, which is also east of Linton. Perhaps your relative worked there?
You will find that Victorian birth record of the 1880s are very detailed, and they record parents' names, where they came from, and mother's maiden name and age when born. This can be very useful in helping you to search further back in the GRO.
When searching I have found that ancestors sometimes varied the spelling of names, so it's worthwhile trying a number of different ways of spelling names if at first you don't succeed.
I hope this helps. Good luck with your search!
Peter
p.s. If you give us his name we might be able to give you more help.