Yes, you can use a custom subdomain setup for your G Suite. All you need to do is to setup an MX record for subdomain.yourdomain.example and point it to the Google's mail servers. The specific procedures are documented on setting up MX records for G Suite Gmail
Pretty much it should look something like:
First of all. I would disagree on using store.siteinquestion.net. Instead you should use store.siteinquestion.com.au. This has to do on keeping a consistent identity across both website and store front.
To accomplish that you need to point the A record on your domain registrar to the IP of the Google Server.
Regarding the use of subdomain/domains. What you ...
If the brands are related to each other, like an Apparel company who own multiple brand names, and the audience segment is the same, then you can go with subdomains.
Pros of subdomains:
Branding and niche authority are maintained.
You can more easily link between your various subdomains.
It is cheaper and easier to manage a website with one main domain and ...