Yes, the two children would still be balanced on the seesaw if it were brought to the moon, assuming their weights remain the same, and the seesaw is identical in both locations.
The reason for this is that balance on a seesaw depends on the principle of torque, which is the product of the weight of each child and their distance from the pivot point (fulcrum). While the gravitational force is weaker on the moon (about 1/6th of that on Earth), the ratio of their weights and distances from the fulcrum remains unchanged.
So, as long as the seesaw and the positioning of the children do not change, they will continue to balance each other perfectly on the moon.