to move the dot you need to delete the dot by painting over it in the background colour and then showing it at the next position, then you need to check the screen with point to find when the colour isn`t zero, that means you are about to plot over something else, and since the something else must be the box then you can draw another box over it in black ink to make it disapear.
but to be honest all of that is giving yourself a lot of grief, why not just use sprites and the built in sprite collision?, far easier and far less trouble to convert to a first full game, plus the 2D commands are more included for legacy than creating games in, unless you plan to make some older "vector graphics" game anyway.