climbing

C has started climbing on things, as if it were here lifetime goal. When we put her on the dining chair, she wants to climb on to the dining table and empty the salt/pepper shaker. If D leaves her on the potty for a minute, C would hold onto the potty water tank, and then climbs onto the washbasin and sits in it. She goes on to play with the water tap and water. We are concerned that she might slip off the sink when she climbs up. We try to keep the toilet door closed all the time.
She climbs up and down the stair without much problem. But does it one riser at a time. The new house stairs may not have a gate, but has carpet treads. However, the new stair is gonna be steep and higher...