A TEFL qualification is a must, especially if you want to teach in Japan. You can get away with not having one in China and possibly other places in Southeast Asia, but it is worth getting one to get a quality job (better hours, better pay, return airfare, etc.) and also to have an idea of what to do once you get in the classroom.
TEFL courses vary, but most are around 4 weeks intensive. I recommend going abroad to do the course. I did mine in Bali and practiced teaching in the local community. I know other people who did their courses in Bangkok and Ho Chi Minh, and they all had good experiences.
Most contracts are for one year, but you might be able to find something shorter. Most language schools hire year-round, so I wouldn't worry about the start of the school year. For Japan, I recommend looking for jobs at Ohayosensei
All the best!