Your booking page has an address on Friday Scheduling that works from the day you set up and needs nothing from you. Using your own domain instead is optional, and it is a presentation decision rather than a functional one — the page, the bookings and the reminders are identical either way.
It is worth doing if you already own a domain, if you print it on cards and signage, or if you would rather clients saw your business name in the address bar. It is not worth buying a domain for on your first week; a working booking page shared everywhere beats a prettier address nobody has yet.
Setting it up means changing DNS records at whoever you bought the domain from, using the values we give you. It is a five-minute job on their side and then a wait — DNS changes can take a few hours to settle, so do it on a quiet day rather than the morning of a launch.
Keep the domain registered and renewed. A domain that lapses takes your booking page's address with it, and the renewal notice usually arrives in an email address you no longer check.
Availability depends on your plan. If the option is not in your settings, that is why.