COVID-19 vaccine development has been widely awaited, but concerns around acceptance and political polarisation prevail. We sought to determine the willingness of Australians to take a (then prospective) COVID-19 vaccine, compared with their previously recorded opinions about other vaccines. We also sought to determine reasons for hesitancy, levels of support for possible government mandates, and the political basis of support. We surveyed 1200 Australians, including 898 participants in a panel previously asked in 2017 about vaccines and mandates. In all, 66% of respondents indicated they would take a coronavirus vaccine, less than the 88% who in 2017 agreed that vaccines are safe, effective, and necessary. Also, 70% of the respondents who indicated hesitancy were concerned about the safety of the vaccine if it was developed too quickly, and 73% of all respondents agreed that the government should require a coronavirus vaccine for work, travel, and study. This is lower than the 85% who agreed with the childhood vaccine mandate in 2017, but slightly higher than the number of respondents who indicated that they would definitely be willing to take the coronavirus vaccine themselves. Older respondents, higher income respondents, and respondents who vote for major parties were all significantly more likely to take a coronavirus vaccine and to support government requirements.