Wearing a life jacket is mandatory in all victorian waters and form most of the rest of Australia (check your local rules) - you should have one on!
If you are out in your recreational kayak - sit on-top, flat water / estuary kayak or even a SUP - these are affordable life jackets that sit close to the body and are not as bulky as a life jacket you might want for sea kayaking / touring.

Make sure that whatever you get it is suited to the kayaking you are doing and has a certification for watersports(Aust Standards, ISO or US Coast Guard).

Life jackets for children will have a crotch strap for the littlest paddlers, so that they don't slide out when they are swimming.