A lady's chaperone was, formally, supposed to act as an example of decorum to an unmarried woman and could give advice on fashion, manners and in domestic situations, assist with receiving guests. A chaperone also escorted an unmarried younger woman to balls and on visits.
So I don't think a father could act as a chaperone to a daughter, at least by himself with an older daughter. A father was the family's authority for giving or refusing permission and had the main disciplinary role, imo. However, a father or older brother could select a companion for a single woman.
As I recall, widower Sir Walter Elliot requested the widowed Mrs Smith to accompany them to Bath to act as companion, and presumably chaperone his unmarried daughter, Elizabeth. (Per)
General Tilney is a widower and his unmarried 20 year daughter accompanies him to Bath. At assemblies, a friend of Miss Tilney's deceased mother, Mrs Hughes tends to remain near to Eleanor. (NA)
Hmm...the nearest example I can think of a father being a 'chaperone'- Sir William Lucas escorting his daughter Maria Lucas with Elizabeth Bennet in the carriage to Rosings (P&P)
I think the comment was Jane and Elizabeth Bennet are mature enough in their behaviour to do without close supervision at a local Assembly. Of course, Elizabeth and Jane are older and better behaved than some younger women who are married and yet, officially can act as chaperones like Lydia Wickham. The foolish Mrs Foster married at a very young age and chaperones Lydia at Brighton, but I'm unsure of her actual age; younger than Jane or Lizzy ?
However, according to Regency era etiquette as Jane and Elizabeth are unmarried young women but of marriageable age, they formally require a chaperone such as their mother or aunt.
Similarly, the sophisticated Miss Bingley, whose in her early 20s', requires her married sister Louisa Hurst to act as a chaperone for her at balls.
Out of interest, the only example I can think of a Regency era lady not requiring a chaperone is Jane Austen. When Miss Austen visited the Prince Regent's librarian at Carlton House circa 1814, her mother apparently decided she did not require a chaperone as Jane was nearly 40 years old and considered to be well, of an unmarriage age!
Below, I've linked an earlier discussion on Chaperones which hopefully will give you a better idea on the need for a chaperone by young ladies in the Regency era. See former L&T host JulieW's post on chaperones in JA's novels.