Will I lose my statue? Will I lose my Hall of Monuments point progression? Or is it safe? What happens if I destroy a minipet dedicated at the Hall of Monuments?
Nothing, once you have dedicated the minipet to your monument, you can trade, give away, or destroy the minipet with no consequences. Your monument statue will always be there and count towards your account. It just can't be rededicated by anyone else. Typically dedicated minipets are worth only 10-20% of the undedicated value because of this reason.