This is one of the greyer areas. Looking through the results for a Google search for "holds the title doctor" does not turn up a lot of results, but
(1) as far as I've checked, almost all of those results where 'doctor' is part of a more explicit title have 'doctor' capitalised:
- ... holds the title Doctor of Science ...
- ... holds the title Doctor of Jurisprudence ...
- ... holds the title Doctor of Chiropractic ...
- ... holds the title Doctor Honoris Causa from Blaise Pascal University ...
(amongst others) while
(2) most of the few examples I've found where 'doctor' is stand-alone use lower case, for example:
any audiologist who holds the title doctor has earned a clinical doctorate in audiology [American Academy of Audiology]
As above your passport doesn't have a Dr field, it says 'holds the title doctor' on the official observations. [Reddit; Google]
Note that none of the above uses italicisation, which (with capitalisation) would have been my choice for your example sentence until a few years ago. And inverted commas (and quite possibly no 'of') would have been unsurprising in the not too distant past. This remains a style choice, but it's usually best to adopt the most usual practice in these matters.