Update: This information is from the Australian Department of Foreign Affairs website:

Australia established diplomatic relations with Kazakhstan in 1992. Australia opened an embassy in Almaty in 1995, but closed it in 1999 due to resource constraints. Kazakhstan opened a Consulate in Sydney in January 1996, but closed it in March 2003 for similar reasons. In January 2005, Australia established an Honorary Consul in Almaty. Australia’s current Ambassador to Kazakhstan is Mr Robert Tyson, resident in Moscow.