There is no problem in applying for admission to BEd in your case. After completing it, you will have options for teaching in various categories in the schools.
If you have a good academic career, you can even go for tests like NET etc which will give you opportunity for applying for lecturership in the colleges.
If teaching is your interest area then it makes sense to go for BEd. However, as per your qualifications, you have presently many other options and the opportunities to exercise ranging from IT jobs in the industry to Govt jobs at center and state Govt levels.
Meanwhile, join some small job, whatever it is, to gain the practical experience and also to keep yourself busy. You can even consider BEd through correspondence mode or in evening college mode if you want to do it as a sideline to your job.
Please remember that to use your academic knowledge you must keep yourself busy in a job where you can refresh it. From that angle, a teaching job is a good choice.
Knowledge is power.