The situation in Australia's ACT is different:
In Australia's Federal Parliament, the ACT is represented by five federal members: three members of the House of Representatives represent the Division of Bean, the Division of Canberra and the Division of Fenner, and it is one of only two territories to be represented in the Senate, with two Senators (the other being the Northern Territory).
I'm not seeing any evidence of any recent campaign to change this.
EDIT based on @JoeC's comment: Some historical background from another Wikipedia article:
The division was created in 1949 and included the whole of the city of Canberra and surrounding rural areas.
Prior to 1949, the Australian Capital Territory (ACT) had no representation in the Australian Parliament. The ACT's first member was elected at the 1949 federal election. However, until 1966 he could only vote on matters relating to the ACT and did not count for the purposes of forming government. In 1966, full voting rights were granted.