One typical way to tweak the perlin noise terrain to make it look right is to simply add (or subtract) a constant offset from the function, thereby literally raising or lowering the sea level. If you raise it, you should get a lot more water and much fewer tiny islands. Also, your perlin noise does seem a bit off, are you sure you are reducing the amplitude properly as the frequency increases? You seem to have some pretty sharp peaks, normally perlin noise is a bit smoother.
Another more advanced method is to take your mesh and smooth it out a little bit to simulate erosion (such as an average, or a rule which lowers a point's height depending on neighbouring heights) which would tend to get rid of the small islands while only eating a little bit at the large continents. It is mostly tweaking, really, there is no magic setting that'll make things look earth-like.