Beyond cats, this quote from a friend of Jane Austen, regarding the horrors that would ensue should a woman include her real name with a published work, is quite interesting. The result of such would be "to be pointed at -- to be noticed &... commented upon--to be suspected of literary airs--to be shunned as literary women are..." Jane Austen's name did not appear in her lifetime on her novels.
We do have a cat metaphor, and let me mention a bit of detail leading up to it, from Jane Austen, Her Life and Letters: A Family Record written and edited by William Austen-Leigh, and Richard Arthur Austen-Leigh (1913). The correspondence is with her sister Cassandra.
Thursday [September 16, 1813, ...]
Thank you, my dearest Cassandra, for the nice long letter...
We . . . went to Wedgwood’s, where my brother and Fanny chose a dinner set. I believe the pattern is a small lozenge in purple, between lines of narrow gold, and it is to have the crest.
With love to you all, ...I remain,
Yours very affectionately,
Godmersham Park : Thursday [September 23, 1813]. My Dearest Cassandra—Thank you five hundred and forty times for the exquisite piece of workmanship [a letter] which was brought into the room this morning, while we were at breakfast, .... and which I read with high glee, much delighted with everything it told, whether good or bad. It is so rich in striking intelligence that I hardly know what to reply to first. I believe finery must have it.
I am extremely glad that you like the poplin. I thought it would have my mother’s approbation, but was not so confident of yours. Remember that it is a present. Do not refuse me. I am very rich.
Let me know when you begin the new tea, and the new white wine. My present elegancies have not yet made me indifferent to such matters. I am still a cat if I see a mouse...
The picture of women turning into cats when they see a mouse, goes back to the Greeks, over two thousand years. The presumption is that women are essentially cats and their true nature is revealed in the irresistible circumstance of spotting a mouse.