Can I do M.A. After B.Ed 1st year?

You can pursue Masters as it only needs graduation means Bachelors degree for Masters degree.

Yes you can. For e. g M.A. In distance mode and B.Ed in regular mode or B.Ed in distance and M.A. Regular. But it would not be a good strategy. I suggest you to appear for UGC NET during last year of M.A. And appear for B.Ed entrance simultaneously. This could be a good strategy. Best wishes.