Perhaps Elizabeth shares more traits with her father than we think. Miss Austen gives us some clues. From Ch 1 concerning Mr. Bennet:

"......Mr. Bennet was so odd a mixture of quick parts, sarcastic humour, reserve, and caprice....."
We can certainly attribute to Elizabeth "quick parts, humor, and caprice" can we not?

Ch 60 gives us a few more clues:
"......Elizabeth's spirits soon rising to playfulness again, she wanted Mr. Darcy to account for his having ever fallen in love with her....."
AND.....
"...Now be sincere; did you admire me for my impertinence?"
AND A LONG ONE....
".....Georgiana had the highest opinion in the world of Elizabeth; though at first she often listened with an astonishment bordering on alarm at her lively, sportive manner of talking to her brother. He, who had always inspired in herself a respect which almost overcame her affection, she now saw the object of open pleasantry. Her mind received knowledge which had never before fallen in her way. By Elizabeth's instructions she began to comprehend that a woman may take liberties with her husband which a brother will not always allow in a sister more than ten years younger than himself.

I perceive from some of the above quotes that Elizabeth enjoys keeping people slightly off-balance and wondering what she is up to or thinking. Mr. Bennet, when he waited on Mr. Bingley for the first time and did not tell his family is typical of him playing with people's minds.

Another telling evidence is also from Ch 61:
".....Mr. Bennet missed his second daughter exceedingly; his affection for her drew him oftener from home than anything else could do. He delighted in going to Pemberley, especially when he was least expected....." Isn't it just like Mr. Bennet to show up unannounced? Sorta like father like daughter; They're so fond of each other because they are so much alike.

Poor Darcy, it was the "liveliness of her mind." Since Mr. Bennet had a standing invitation at Pemberley, I would assume Mr. Darcy liked Mr. Bennet very much also because he shared some of the quirky qualities of his favorite daughter.