This study aimed to investigate the impact of sociodemographic characteristics on pet owners’ concern about the transmission of zoonotic disease and SARS-CoV-2, and to describe owners’ perceptions of veterinarians and physicians as resources for zoonoses information. Between September and October 2020, 1154 individuals completed an online survey via Qualtrics. Binary logistic regression models were used to examine the associations between owner demographics and perceptions of zoonoses and SARS-CoV-2. Most participants were minimally concerned about their pets contracting or transmitting zoonotic diseases or SARS-CoV-2, although perceptions of risk differed based on age, race, and education. Older participants were typically less concerned about the transmission of zoonotic diseases and SARS-CoV-2. Considering where participants obtained information about zoonoses, pet owners were more likely to contact their veterinarian for advice (43%) than their physician (17%). However, 17% of pet owners struggled to access veterinary care, and 51% said their access to veterinary care had become more difficult during the COVID-19 pandemic. Our findings highlight a need for further education about zoonoses and SARS-CoV-2, and suggest veterinarians may play a key role in these communications. The results also emphasize the need to address access to care issues in veterinary medicine.