The COVID-19 pandemic has made a huge global impact and cost millions of lives. As COVID-19 vaccines were rolled out, they were quickly met with widespread hesitancy. To address the concerns of hesitant people, we launched VIRA, a public dialogue system aimed at addressing questions and concerns surrounding the COVID-19 vaccines. Here, we release VIRADialogs, a dataset of over 8k dialogues conducted by actual users with VIRA, providing a unique real-world conversational dataset. In light of rapid changes in users' intents, due to updates in guidelines or in response to new information, we highlight the important task of intent discovery in this use-case. We introduce a novel automatic evaluation framework for intent discovery, leveraging the existing intent classifier of VIRA. We use this framework to report baseline intent discovery results over VIRADialogs, that highlight the difficulty of this task.