It's been a year since you posted your message - you've probably worked it out by now. But just in case ...
It is possible to access NSW Birth, Deaths & Marriages on the internet -
www.bdm.gov.au - and order copies of certificates online.
A quick search shows that a William Henry Thompson married Sarah White in 1873 in the Inverell district of NSW.
Two children are recorded as having being born - Henry, 1875, at Molong NSW and Anne Sarah in 1880, at Coonamble, NSW. They probably survived childhood - no deaths recorded in their names.
William and Sarah's deaths and her birth are a bit trickier to track down. You really need their parent's christian names but you can narrow down the possibilities with a bit of sleuthing. For example, there are a few Sarah Ann/e White births recorded. It is quite likely that, having named the son after the father, the daughter was given the mother's names in reverse order.
If you order a copy of William and Sarah's marriage certificate, it will give you the place of birth, occupation, and names of parents of each. This will give you the information you need to access information regarding death.
The birth certificates of Henry and Anne Sarah can also be ordered.