Australia adopted hard lockdown measures to eliminate community transmission of COVID-19. Lockdown imposes periods of social isolation that contributes to increased levels of stress, anxiety, depression, loneliness, and worry. We examined whether lockdowns have similar psychosocial associations across rural and urban areas and whether associations existed between happiness and worry of loneliness in the initial wave of the COVID-19 pandemic in Australia. Data were collected using the “COVID-19 Living Survey” between 13 and 20 May 2020 by BehaviourWorks Australia at the Monash Sustainable Development Institute. The mean self-reported feeling of happiness and anxiousness (N = 1593), on a 10-point Likert scale with 0 being least happy or highly anxious, was 6.5 (SD = 2.4) and 3.9 (2.9), respectively. Factors associated with happiness were older age and having a postgraduate education. Participants worried about becoming lonely also exhibited reduced happiness (estimate = −1.58, 95%CI = −1.84–−1.32) and higher anxiousness (2.22, 1.93–2.51) scores, and these conditions remained associated after adjusting for demographics. Interestingly, worry about loneliness was greater in rural areas than in urban communities. The negative impact of the COVID-19 lockdown on rural youth and those less-educated was evident. Participants in rural Australia who were worried about becoming lonely were reportedly less happy than participants in major cities. This dataset provides a better understanding of factors that influence psychological well-being and quality of life in the Australian population and helps to determine whether happiness may be an associative factor that could mitigate self-feelings of anxiety and worry about loneliness.