Controversy around the safety and efficacy of COVID-19 vaccines may lead to low vaccination rates. Survey data were collected in April and August 2020 from a total of 2343 Australian adults. A quarter (n = 575, 24%) completed both surveys. A generalized linear mixed model analysis was conducted to determine whether willingness to vaccinate changed in the repeated sample, and a multinominal logistic regression was conducted in all participants to determine whether willingness to vaccinate was associated with demographics, chronic disease, or media use. Willingness to vaccinate slightly decreased between April (87%) and August (85%) but this was not significant. Willingness to vaccinate was lower in people with a certificate or diploma (79%) compared to those with a Bachelor degree (87%), p < 0.01 and lower in infrequent users of traditional media (78%) compared to frequent users of traditional media (89%), p < 0.001. Women were more likely to be unsure if they would be willing to vaccinate (10%) compared to men (7%), p < 0.01. There were no associations between willingness to vaccinate and age, chronic disease, or social media use. Promotion of a COVID-19 vaccine should consider targeting women, and people with a certificate or diploma, via non-traditional media channels.