The COVID-19 pandemic has been ongoing for close to a year, with second waves occurring presently and many viewing a vaccine as the most likely way to curb successive waves and promote herd immunity. Reaching herd immunity status likely necessitates that children, as well as their parents, receive a vaccine targeting SARS-CoV-2. In this exploratory study, we investigated the demographic, experiential, and psychological factors associated with the anticipated likelihood and speed of having children receive a SARS-CoV-2 vaccine in a sample of 455 Canadian families (857 children). Using linear mixed effects and proportional odds logistic regression models, we demonstrated that older parental age, living in the Prairies (relative to Central Canada), more complete child and parental vaccination history, more positive attitudes towards vaccines generally, higher psychological avoidance of the pandemic and a greater tendency to prioritize the risks of the disease relative to the risks of side effects (i.e., lower omission bias), were associated with higher likelihoods of intention to vaccinate participants' children. In some models, subjective evaluations of proximal COVID-19 risk and higher levels of state anxiety were associated with increased likelihood of having children vaccinated. Faster speed of intended vaccination was predicted by a similar constellation of variables, with higher SES emerging as a trend-level predictor of vaccination speed. Results are discussed with respect to public health knowledge mobilization.