Damage dealt to Anya is tracked even if Anya has indestructible. For example, if Anya is dealt what would be lethal damage and Anya loses indestructible (perhaps because each opponent's life total is too high), it will be destroyed the next time state-based actions are performed. However, the check for whether a creature dealt damage by a source with deathtouch is destroyed happens only the first time that state-based actions are performed after that damage-dealing event.