I'm not the expert some here have become through experience, so add a grain of salt to my recommendations.
Set up a meeting with the advisor sooner rather than later, either just a few minutes to share this and stress how it should not impact your work, or mentioned during a meeting on some other aspect of your work under her supervision. Since you anticipate her support and hope to continue with her in Boston*, she deserves to know early on. It's possible she may have noticed small changes even before you committed via HRT, like mannerisms, no-gender clothing choices, or shaped brows or nails, so she may not be surprised.
Whether you share this with the PhD committee or she does, and when and how, might be something you discuss and decide together. I don't know her, of course, but it's possible she'd be at ease doing this for you, or with you. At six months of HRT, the physical changes will probably be apparent. The committee should know well before your defense, and probably before it's obvious to anyone to actually looks at you closely, even if you are presenting your public self as androgynous at that point rather than female.
Maryn, handing you the salt shaker
* If you're in Boston for a year, try again to meet up with my daughter?