Can my partner and children come with me on a Government Authorised Exchange visa?

Your partner and children under 18 may join you if they meet the dependant requirements. Each person applies separately and pays their own application fee and healthcare surcharge.

Because this is a short-term route, dependants' permission is tied to your visa and will end when yours does. Factor that into family plans, since this route does not by itself lead to long-term residence for any of you.