The piers are the North and South piers which have formed the entrance to the original docks for over four hundred years. Obviously they will have been rebuilt many times over the years and the amount showing above the water will be dependent on the state of the tide. Today, they comprise the entrance to the Tidal Basin with the developments from the late nineteenth century onward extending seaward, as seen in the Marina diagram at the foot of this post.
A similar view to that posted by Colin is a canvas print I purchased some time ago, entitled Dover Harbour by Edward William Cooke, 1811-1880. Again, there is a sailing ship being followed through the pierheads by one of the early steam packet boats. The first of these was the Rob Roy in 1821 which was followed by a succession of similar small paddlewheel packet boats carrying the mail. There are numerous illustrations showing these vessels with the very tall single funnel characterising the ones in the pictures.
Full size image on my fotopic site at:
http://shipsintheportofdover.fotopic.net/p65145172.html
Some charts depicting the development of the harbour and showing the North and South piers: