It's effect can only be activated in the draw phase only but id doesn't have to be activated during the next turn, you can choose which one, one time only. As per the rulings on Dasher...
You can activate this effect when you draw a monster during your Draw Phase because of a card effect such as "Reload" or "Heart of the Underdog".
You do not declare the activation before you draw, you activate it..."When you draw a monster"