Is it permissible to ask the advisor if she has funding to support me as a postdoc for a year?
Regarding the main question, I refer to xLeitix' excellent answer to a similar question.

Addressing the specific parts of your situation, I see two likely reasons why your advisor hasn't offered you anything yet:


publication record - in most fields, securing a post-doc position requires a reasonably good track record in publications. If your publication output during your PhD was not on par, she may be worried if an academic career is for you.
lack of funding - to offer you a position, your advisor would need to have funding for you readily available. This would be most likely if she recently won a grant. You should ask her about that. If she has no funding for you now, you can ask if she knows any other PIs who are looking for post-docs, which might be more likely. 


You can also consider writing your own grant proposal for a post-doc position; some countries have dedicated funding options for that. (However, the decision process may take half a year or more.)