As your passport will still be valid for more than six months when you go in for stamping, that should not be a problem. The issue would potentially be with your I-94, but that won't be an issue at the time of stamping and you'll have your renewed passport before re-entry. As you will have your new passport with you when you re-enter the U.S., the immigration officer should approve your I-94 based upon your having the new passport which should be valid for many years past the expiration of your visa. Your I-94 will be stapled to your new passport, even though your visa is in the old passport -- don't lose the old passport.
As there may be details about your situation of which we are not aware, you should consider consulting your employer's immigration lawyer about your situation.

