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 as a 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 a given dialogue system. We use this framework to report baseline intent-discovery results over VIRADialogs, that highlight the difficulty of this task.