I commend you for wanting to volunteer with the Red Cross. I am a Red Cross volunteer nurse and went to New Orleans following Katrina.
I don't know if you will be able to work on the Disaster Health Team as a student nurse as I believe it requires a license. But there are other teams that you can work on that will be just as rewarding. Be sure to get a lost of all of the disaster teams. Also, get a calender of all the training opportunities. There will be lots of opportunities for local volunteer work which is good training for larger disasters. Once you become a volunteer you will get called for all sorts or disasters, from local house fires, wild fires, flooding, etc.
There is also a need for volunteers to teach classes. You might want to look into that.
Feel free to pm me or post other questions here.