This laptop should be great for your son to play on. I use a computer with 4gb of ram and minecraft runs smoothly. As long as you have 1gb free (and no other programs running, at all 2gb to be safe) minecraft will run as well as a 64gb laptop. The reason being is because when minecraft is run, by default, it is allowed only 1gb of ram to use. If, however, this is not enough, you can allow it more memory. Simply go to editprofile->advanced->then the box with the random letter (check the box above it first) and copy the text in the box. Then create a file named "<whatever you want here>.bat", right click the file, go to edit, then type...
java <then the text that was in the box>
This will only open minecraft with the 1gb but at the end of the text, it says 1g, change that to 2g or 3g, or whatever you want.
Note: To make minecraft run off of more than one gb, a 64bit computer is recomended (64 bit is now the standard compter)
I hope your son enjoys minecraft :)