In Austria, consent to receiving vaccines is regulated at the federal state level and in Tyrol, children aged 14 years are allowed to consent to receiving vaccination. In August 2017, we investigated determinants associated with vaccine hesitancy, having been vaccinated against measles and human papillomavirus (HPV) and the intention to vaccinate among schoolchildren born in 2002 and 2003. Those who consider measles and HPV a severe disease had a significantly higher intention to be vaccinated (prevalence ratio (PR) of 3.5 (95% CI 1.97–6.32) for measles and a PR of 3.2 (95% CI 1.62–6.35) for HPV). One-third of the participants (32.4%; 95% CI 27.8–37.4) were not aware that they are allowed to consent to receiving vaccines. The most common trusted source reported by respondents (n = 311) was the medical doctor (80.7%; 95% CI 75.7–84.7). The main finding related to the aim of the study was that the proportion of objectors is below 4% and therefore it should still be possible to reach measles elimination for which a 95% uptake is necessary. Although the proportion of objectors is not higher compared to adults, we recommend to intensify health education to increase health literacy.