A population’s desire to take the COVID-19 vaccine is an important predictor of a country’s future pandemic management. This cross-sectional study examines the impact of psychological and sociodemographic factors on attitudes toward and intentions to take the COVID-19 vaccine among students and faculty at four colleges of health professions and sciences at Qatar University. The data were collected through an online survey using Google Forms. The survey was distributed through various online platforms. Data analysis was conducted using Stata 16. Of the 364 participants, 9.89% expressed a high mistrust of vaccine safety, and 21.7% were uncertain about their levels of trust; 28% expressed strong worries about unforeseen side effects, whereas 54.95% expressed moderate worries. Furthermore, 7.69% expressed strong concerns and 39.84% showed moderate concerns about commercial profiteering. Approximately 13% of the participants expressed a strong preference towards natural immunity, whilst 45.33% appeared to believe that natural immunity might be better than a vaccine. Importantly, 68.13% of the participants intended to receive the COVID-19 vaccine once it became available, compared to 17.03% who were uncertain and 14.83% who were unwilling to be vaccinated. Our findings differ from the data on vaccine hesitancy among the general population of Qatar. We argue that this gap is due to scientific knowledge and domain of education. Furthermore, although knowledge and awareness may affect vaccine attitudes, mental health and sociodemographic factors play a role in shaping attitudes towards vaccines.