The terms say that we can only have one account, so I'm assuming I can't just quit this account and start a new one. Is there a way to close an account so that we can start a new one up?

Sadly, no. x:

Players will have to stick to the account they made. The common thing that admins have said is that in the future, they'll implement a feature that resets account progress. Otherwise, for now, you'd have to stick with your account.

The nearest thing that players can do to reset their progress is release their pets manually and ask an admin for a name change, I think.