This book title will have to be found to have "secondary meaning". This can be a tough hurdle for the publisher/author. It will typically require that a significant portion of the public knows of the name and associates it with the book. Not a question that can be answered without more facts. If I had a gun to my head I'd say that given the rather short duration of this book's circulation and the niche nature of it, the existence of secondary meaning, as a matter of law, is less than 50%. Too close to be good legal advice I'm sorry to say.
1st of all, don't use real trademarks or domain names or names of people on this public forum, which everyone, including this author, can read.
A domain name is a piece of intangible property, and it can function as a trademark if it's used as one, but it can also be just a domain name.
A website is a creative work that can use a trademark to brand goods or services, and the website pages can be copyrighted.
If your website's not live yet, it definitely hasn't served to use the word as a trademark, because a trademark has to brand the source of some particular goods or services. If your site is up and running, you're presumably using the domain name as a service mark for your education/informational/entertainment services, which would be international TM class 41.
A book's title isn't copyrightable, and it's only rarely trademarkable. The series "---------- For Dummies" is an example of a kind of book title that can function as trademark since it indicates in consumers' minds the course of the book. Books are paper goods that are trademarked in class 16.
Trademark infringement requires consumer confusion. For there to be confusion here, people wanting to buy this Dr.'s book would have to mistakenly go to your website, find no book, and not keep looking to find the book. Then the Dr. would have a claim against you for TM infringement, assuming he was the 1st user. And if someone wanted information like the kind available on your site but instead mistakenly found and bought the Dr.'s book, then you'd have a claim against the Dr., assuming you were the 1st use. The topic of your site and his book are somewhat related, but given the difference in your services and his book, it seems unlikey that a consumer would be confused.
But maybe this author has or will have a website with a domain name that's confusingly similar to yours, as well as other goods and services. It's possible that your website will have other goods for sale. The potential for consumer confusion does exist.
Avvo doesn't pay us for these responses, and I'm not your lawyer just because I answer this question or respond to any follow-up comments. If you want to hire me, please contact me. Otherwise, please don't expect a further response. We need an actual written agreement to form an attorney-client relationship. I'm only licensed in CA and you shouldn't rely on this answer, since each state has different laws, each situation is fact specific, and it's impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue.