Hello Lisa.
Though I cannot help with the Wiltshire origins of your HEWETT couple, I can make a couple of suggestions for your searches in Australia,
At the top of the Australian Board page is a list of Australian Resources and if you look at NSW, you'll see where you can look for BMD events. If you find early ones, they will be simple church records as it was not compulsory to make registrations until 1858 in NSW, so there will be births and so on that will not necessarily be recorded at all.
If you have an Ancestry account, there are a couple of trees put up there, but the information may not be reliable without good documentation.
I do see one tree there that shows Eliza had something over 20 children. Might be open to question.

Trove newspaper Archive will possibly hold items about them and their descendants too.
It looks as if Eliza's maiden name was OVENS or OWENS and there is a marriage document recording their union in Wiltshire on Ancestry.
It shows Mary Ann OVENS was a witness to the event.
Here are a couple of news items I found on a quick Trove search about their NSW lives.
Here is a death notice for Eliza HEWETT inserted by her SIL WH Jennings in 1873
William H Jennings had married Mary Ann, the daughter of the HEWETT couple in 1870
Also on the same page a notice from SIL, R Medcalf.
Eliza’s last address is given.
https://trove.nla.gov.au/newspaper/article/13316565?searchTerm=%22w%20h%20jennings%22Marriage
1321/1870
MIDCALF Robert G
HEWETT Catherine E
REDFERN
Death of Catherine
MEDCALF Catherine E
3636/1928
Father EDWIN
Mother ELIZA
At MANLY
I'm sure there will be more to find, but I don't know what you are specifically seeking.
You might like to look at part of the Log of the Woodbridge 1838
https://www.xroyvision.com.au/andrews/history/hist4.htmSue