How can I click "Do It!" button with keyboard?
If there's just one option hitting Space or Enter should do the trick, as the button should be preselected. If there are more than one option you could tab between them by enabling  All Controls under System Preferences / Keyboard / Full Keyboard Access. 

When tabbing through, a subtle blue glow will highlight the tabbed component. Hitting Space will use it, while hitting Enter will use the default option.