In Australia, the requirements for booster seats are based on both age and size. For a 4-year-old, they must use either a forward-facing child restraint with an inbuilt harness or a booster seat with a lap-sash seatbelt or harness. (The former is ideal, known as a Type G seat for example a Maxi Cosi Tuva).
As for whether the booster needs to be anchored, there is no regulation enforcing this - you can use a "Tethered" or "Untethered" style - but to clarify, if the booster has an upper tether it must be used. If you are hoping to utilise an untethered style booster, there aren't too many on the Australian market but two common ones are the SafeNSound Tourer (which we would prefer as it has the anti-submarining device built in) or the InfaSecure version which is still a good seat in context.
The challenge you will have for a 4 year old is at that age they frequently don't meet the height requirements so just double check that before you transport as the child may still need to be in a 5 point harness (age is a guide in Australia, primarily seated height is the key factor in determining safe transport).
Whichever child seat you end up using, we recommend checking the manufacturer’s guidelines for that specific seat, as well as ensuring it complies with Australian Standard AS/NZS 1754.
