[ST03-005] - Dracule Mihawk (Starter Deck 3: The Seven Warlords of The Sea)

If I have 1 or less cards in my deck, can I use this Character to attack if it has a DON!! card given to it?

Yes, you can. However, since the [When Attacking] effect is always activated and requires a player to draw 2 cards whenever possible, if the deck is reduced to 0 cards as a result, the player with 0 cards in their deck will lose the game.