Why do you want to change your dot size, when you can chose filled circles as symbols?
Try this command:
plot ... with points pointtype 7 pointsize 5
Here
pointtype (or pt) allows you to select different symbols (Each terminal has a default set of line and point types, which can be seen by using the command test, e.g. pngcairo: pt 5 would be a filled square)
pointsize (or ps) allows you to control the size, as you had mentioned before.
I think the difference between a dot and a point is, that dot will always be a pixel-dot. If you are looking for more flexibility, points will allow that.