... But as soon as she has found her feet I have no doubt that she will fire me.
The company owners have fallen for her charm and image, but I am wondering if there is anything I can do to unseat her and bring on an early departure before she ruins the company.
Read what Lucy Kellaway, "agony-aunt" of the Financial Times (London), answered:
You complain that your boss is clueless about the business. Of course she's clueless - she's only been with the company for five minutes. Everyone is allowed to be a bit clueless at the beginning, especially if they have come from another industry.
Ignorant people are worse
The more interesting question is whether she is healthily aware of her cluelessness and is taking steps to rid herself of it. The dangerous people are the ones who are oblivious to their ignorance and charge in making a load of terrible decisions. As you don't refer to any awful decisions that have already been made, I'm assuming that there haven't been any - yet.