Cedula de idendidade - Brazilian identity card

Yes, you should have an Identity Card, which in Brazil is called a "RG", "Registro Geral", if you plan on spending much time in the country.   (If not, it's probably not worth a special trip.)  It looks like your Título de Eleitor, but a little smaller.

RGs are issued at the municipal level, but are valid nationwide.  Next time you're in Brazil, check with the local police to find out where the office is that issues them.

Thanks for your reply, Abthree.
A couple of questions, if I may.
Do you know if the RG has to be renewed like, for example, a passport (every 10 years)?
Do you feel I should be able to obtain a RG in a three weeks time? That is the time I am planning to spend in Brazil next year, with morning lessons to learn some portuguese and free afternoons to move around as a tourist.

The RG is permanent for adults:  adolescents need to renew it every couple of years as they grow, but once you pass 21, that's permitted but no longer required.

If you go to the central identification office in the city where you're studying, they should turn it around in about a week - that's how long mine took after I became a citizen.   Branch offices take longer, so go to the central office.