You’re correct – you’re not subject to the H-1B cap and can indeed change employers (referred to as “portability”) without having to wait until October 1. If you meet the portability requirements, while the new petition is pending you can travel with your old visa and form I-797A receipt notice for the new petition.
If you’d like to further discuss your case or would like me to prepare your new H-1B petition, please contact my office.
Attorney Edward Weiner
http://www.immigration-aux-usa.com