It is not possible to "just" upgrade the wireless modem on your laptop. It is too deeply integrated into the machine to allow for a simple user upgrade, or even a complicated technical one really. What you do need to confirm is that it is capable of connecting with 802.11n protocols on 5GHz to get the maximum connection speed. The current speeds you are getting are not too bad at all although they fall far short of the theoretical maximum.
If you are stuck with 802.11g on 2.4GHz, then you will have to put up with that or buy a new laptop. Six years is twice the normal commercial upgrade cycle, although plenty of home users run PCs that are ten years old or more without any problems.
Last edited by G0ULI; 16th Sep 2017 at 10:04.