That could work for you. Do you have more than one Ethernet port in your room? If not, the issue with the AP is going to be that it will use your one and only Ethernet port. If someone brings in a device that lacks wifi, there will be no way to plug it in.
Consider going with a wireless router instead. It is just an AP that also include additional Ethernet ports. This gives you the option of running both wired and wireless. Cost about the same, and the set up is the same. You still have to set up the AP part of either device. Plus running wired is always faster than wireless, so even if you have a lapop you may want to option of using when wire when speed is important (such as online games or streaming videos.)
Also, you probably already know that you will need a wireless card in your computer or laptop to be able to receive the wifi signal from either the router or an AP. If you have a laptop (tablet or smart phone) there is most likely a wifi card already build into it, However if you have a desktop you will need to purchase a wireless card (internal or USB) for it.
Finally, when purchase the router or AP, make sure that it is an "N" router and not a "G". The reason that they do not provide wifi in dorms is that with all forms of wifi before "N" (A,B and G) there were only 11 channels available and those overlapped with each other so that 1,6 and 11 were the only useable channels. You get 25 routers in a small area (like a dorm) and the signals overlap, conflict with each other, and no one can get on.
With "N" (and the new "AC" which is just beginning to appear), you have over 50 channels and any beyond the first 11 do NOT overlap with each other. You can set your router to a channel higher that 14 (channels 12 to 14 are not available in the US - they were taken away for other uses) and the odds that it will conflict with someone else are small.