Revealing a Dragon card happens as Dragon's Disciple resolves. It is not an additional cost for casting the spell.
Dragon's Disciple
Players can respond to Dragon's Disciple while it is on the stack, but they cannot respond to the choice of whether or not to reveal a Dragon as it enters the battlefield. Notably, that means they can't remove your Dragon from play to prevent Dragon's Disciple from getting the counter once you've decided not to reveal a Dragon card.
A Dragon card is a card with the creature type Dragon in its type line. Similarly, a creature on the battlefield is a Dragon if it has the Dragon creature type. A card that has “Dragon” in the name (such as Dragon's Disciple) isn't a Dragon card unless it also has the Dragon creature type.
Magic: The Gathering · ™ & © Wizards of the Coast · Illus. Lucas Graciano
Card data via Scryfall. Rarix is fan-made; not endorsed by the rights holders.
