Yes, you are eligible for H1B jobs based on your educational qualification.
There is no stipulated time gap for reapply. The only thing is that the H1B quota should be available.
You cannot apply for H1B now as the FY2013 quota got over on 11th June. However, you may identify employers who are eligible to file cap-exempt petitions (like NFP organizations) and petitions can be filed anytime.
If you apply for FY2014 quota which starts in April 2013 and your petition got approved, you can start working in the US from 1st October 2013 or later.