Is USCIS premium processing available for change of status from H4 - > H-1B1 visas?
Yes, but for an H-1B1, the fastest would be to apply directly at the US Embassy in Singapore/Chile.
Your employer needs to retain an experienced immigration lawyer to review all the facts, advise them, and handle the case. Your employer can find one through http://www.ailalawyer.com.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.
While premium process is available for h1b it is not available for h1b1