Your birth date is enough. Wooly works out the exact shape the Moon held the night you arrived — how much of it was lit, and the sign it stood in.
Unlike a birth chart, the Moon's shape barely cares about the hour: it changes by about 12° a day, so your date alone pins how full it was to within about 5 points. Give the time if you have it and Wooly will use it.
A partner, a friend, a child. Wooly puts your two Moons side by side. Their date is not stored anywhere.