-Because your OPT will expire before 4/1/09, you can not work between 4/1/09-10/1/09 even if you get the H1 cap and get H1 application approved. But because you have two-month grace period after your OPT expires, you can stay in U.S. and legally extend the staying to Oct. 1, 2009 if you file the H1 application before 5/31/09 and get your H1 approved.
This answer just applys to the Cap-limit H1. If you change your F1 to H1 sponsored by a non-profit institution, you can work after your H1 is approved.