In my home, I have a Wimax ADSL connection. The router connects to the net through a modem (IDU). I just read about dual band routers. It seems to be they are useful when the router is connecting to the net through internet. In my home, only about 1 to 2 devices connect through Wifi. Other devices use cables. So my question is, will it be pointless to have a dual band router in my setup?
It depends on what the devices are.
For example, if I had 2 tablets, 2 mobile phones, 1 PC and 1 laptop I would not use a dual band router unless I experienced issues.
For an example of when to use it, I have a NAS drive and a media player which can stream wirelessly - this is the ideal time to use a dual band router, effectively given my media center a dedicated line (albeit wireless).
My advice with all of these things is don't look for a solution for a problem which doesn't exist (these things only exist because of things which go wrong), be happy there is no problem with your set up.
So, to answer you, I would leave the router alone and not invest in a dual band.