Amy and Phil Garner have lived in Canberra for almost nine years.
They moved from Palmerston North after Mrs Garner was unable to find work as a social worker. and their children Ella, 6, and Ryan, 4, were born there.
Mrs Garner said the family loved Australia and considered it home but times had been tougher lately. She has had to give up part-time work to care for Ryan, who was diagnosed with autism in August last year.
The National Disability Insurance Scheme (NDIS), which the Garners pay for through an increased Medicare levy, initially approved support for Ryan, which would help pay for early intervention groups, speech therapy and other services. But when it was noticed that his parents were New Zealand citizens, that support was withdrawn.
The Garners have some support from the ACT Government, but that will end next year.