If "Rose Fairy" is added to the hand by a card effect that was activated at Chain Link 2 or higher, you can activate its effect after the chain resolves.
The effect of "Rose Fairy" can be activated not only when the effect of "Dogu", etc. adds it to the hand, but also when it is added to the hand by drawing it with the effect of "Jar of Greed", etc.
Out of Date
↑The latest erratum of this card has Problem-Solving Card Text which does not indicate that it cannot be activated during the Damage Step. All Trigger Effects that cannot be activated during the Damage Step now specifically indicate as such, meaning that this card's effect can be.