If she has H-4 status already, then she doesn't need to file an I-539 just because you change H-1B employers. But if the expiration date of your new H-1B status will no longer match the expiration date of her H-4 status, then you may find it more convenient for your wife to file the I-539 seeking an extension to match your new expiration date now. Otherwise she must do so later before her H-4 status expires (or travel abroad and reenter and get a new I-94 that matches your new expiration date).
It is advisable, though not necessary, to do so.
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.