Can I prevent scheduling appointments that are less than an hour away?

Yes, you can do this using the Event Scheduling step of creating an appointment page.

For example, consider this option - Prevent scheduling appointments less than 2 hours away.  If you select this, customers will not be able to schedule an appointment within 2 hours from the current time as they will only see slots available 2 hours after the current time. 

Note: Click the hyperlink to view the reference screen.