I will be cooking in my dorm this coming year, and I only have an electric kettle at the moment. Is there a way for me to cook rice with only this (i.e. without a stove), or should I just get one of those plastic microwave rice cookers to use in the floor lounge?
Stick to the microwave. Many college dorms are somewhat underwired for everybody bringing high-wattage appliances, have (as yours would seem to ) rules against those, and many college life safety departments will quite happily confiscate high-wattage appliances that are forbidden. Burning the place down is a BIT of a concern. Use the cooking facilities provided (there might even be a real stove someplace in the dorm you can use if you expand beyond the microwave - but if a microwave is all you have, learn to make the most of it.)
Typically an electric kettle is used for boiling liquids and unless you somehow defeat the safety shut off when the liquid boils, which is EXTREMELY DANGEROUS! and absolutely not recommended!! you won't be able to hold a boil.
Ask whether a simple electric rice cooker would be allowed (the 0.6L, 300-400W variety can be had for around $20).
if you can't use a rice cooker or a microwave in your dorm, i would say your only option with the electric kettle is instant rice. all you have to do is add boiling water and cover it for a few minutes.