Apparently the author chose the pseudonym Julia Quinn so that her books were beside Amanda Quick's on the shelves and more people might buy them. Amanda Quick is, of course, hugely successful in this genre but I believe Julia Quinn is a much better author - and this book is a good example of that. If you want complete accuracy in historical detail then this is perhaps not the best author for you - her characters speak with American turns of phrase and rather more 20th century than 19th century worldviews in some cases, but this is common to so many Regencies it's almost de rigueur now - if you can read it as fiction and not history you'll be fine.
"The Duke And I" is the first of the Bridgerton series, focusing on daughter Daphne, and it's a good Regency Romance like many out there (there are also, of course, countless dreadful Regency Romances in print too!) However, like "The Viscount Who Loved Me", the second book in this series, Julia Quinn's characters have a lot more depth than you often see in modern books of this genre.
Yes, we have the usual requirements - balls, gowns, the marriage mart and all the rest of it - but this series delves more closely into family dynamics and character growth. Daphne is the fourth child and the first girl of the Bridgerton family; her father died some time ago and her mother has brought up all eight children in a strong atmosphere of love. This was by no means usual at this time amongst the aristocracy - nannies and nursemaids often functioned more as parent figures than the actual parents - and it has enabled Julia Quinn to build a foundation of strong ties between brothers and sisters that she uses in the books.
And this is the contrast between Daphne, the heroine, and Simon Basset, Duke of Hastings, the hero. His upbringing was completely different - his father rejected him, thinking he was stupid because he stammered, and Simon vowed to avoid marriage and children to get back at his father - the direct line of the Dukes of Hastings would die with Simon. But when he meets Daphne and they discover that a sham betrothal would be of benefit to both of them, their plans start going awry.
What's so good about this book is the way in which the characters begin to understand each other. Daphne learns to stand on her own two feet away from her family - particularly her brothers - and Simon learns to deal with the dreadful legacy that his father has given him. This book often deals with strong emotions and I, for one, think Daphne's behaviour at one particular point is unforgiveable, but I suppose it's this warts-and-all portrayal of two people trying to come to terms with sharing their lives together that is so powerful about the story.