Once I have checked FamilySearch to see which cemetery (and other) records they have for the person I’m researching, and then checked the memorials on Find A Grave and/or BillionGraves, I then check to see if there are other records available online for the cemetery.
I have started to set up a section on my website, Cemeteries in Australia, which has links to sites that have cemetery records in Australia. So far, I have only completed Victoria, the ACT and then NT, but I do have some information for the other states. To generate this list, I checked the links on the Australian Cemeteries website, and I used Google to check for any sites the Australian Cemeteries website might have missed. In my own research, I generally find it quicker to use Google to see what information is available online for a cemetery.
Depending on the type of record, cemetery records might include just the date of burial, or just the date of death, but sometimes the cemetery record also includes the date of birth. In some cases (mainly if the record is from a gravestone) there may just be a year of death or birth.
Not all the cemetery records are available online. Even if there are records available online, if the site just includes the graves with headstones, then the person you’re looking for might not be included. One of the resources I have used are the cemetery records on microfiche at the State Library of Victoria. The other State Libraries and National Library of Australia would probably have similar collections. In some cases, even if there is information available online for a cemetery, the microfiche might have additional information. You can also try contacting the cemetery directly. This is where the Australian Cemeteries website comes in handy, as it includes contact details, and other information, for the cemeteries.