Yes. Most republicans in Australia (remember the term here means 'wants a republican system of government with an elected Head of State (probably called a President)' rather than referring to a political party are socialists. Conservatives tend to be monarchists. There's some crossover (it's certainly possible for somebody to be a conservative and a monarchist) but most of the time, you'll see republican sentiment coming from the left in Australia. It's important to understand that Australia's experience of monarchy has been very different from that of the United States - largely because the British Monarchy learned from its experience in the late 18th century with Americans. It realised that it could not simply trample on the rights of people. For Australians, the monarchy has generally been part of the fundamental protection of our rights - for example, in my state of Victoria, it was Governor Sir Charles Hotham (appointed by Queen Victoria) who in 1854 who stood with up for the rights of the miners who rebelled at Eureka and determined that their grievances were justified and less than a year later, he instituted an elected legislature.
Part of the reason, the left dislikes the Monarch is because in 1975, the Governor-General Sir John Kerr dismissed their messianic idol, Prime Minister Gough Whitlam from office after he started to act illegally - again, an example of the monarchy protecting rights and the constitution.