Hi @Robyn34,
It's nice to be in demand!
Like @Sandra126 said, first to book gets the room. I sometimes get enquiries for the same dates and I treat both the same. If the disappointed person does follow up with a message (they often don't), I just politely thank them for for the enquiry and explain that someone else got their booking in first this time.
I get a few enquiries each year where folk say that they *love* the place and *definitely* want to book but need to check dates/clear it with family/work etc and then I never hear from them again. That's cool, they've found another place, nothing personal. But equally, while I'll pre-approve and offer help, the place goes to whoever books first.
Good luck!
Enda