Do you want to tell her? Is it necessary that she know? Do the benefits of her knowing outweigh the risks?
Legally, you're in a good state for trans protections. In terms of housing law, the amount of rent you pay can't be increased during the middle of your lease if you've signed one, only at the time of lease renewal. She would need a serious reason to ask you to immediately leave (ie. breaking a serious clause in your lease terms, doing extensive damage to the unit, etc.) - and even then, evictions tend to be multi-month affairs. She could however choose not to renew your lease when the time comes. She would not need to give a reason. If you have not signed anything detailing your length of residence and monthly fees, I'd be a little more concerned but legally she'd still have to go through the eviction process with you and that takes several months. Free or low cost legal aid offices handle eviction cases all the time, so I also wouldn't worry too much about legal action unless it gets to that point. It's easily taken care of.
As far as deposits, I'd be a little more concerned about that and I would do everything you can to document how you left the unit when moving out (with date/time stamped pictures). I would document all of your maintenance requests and make sure that anything broken gets fixed prior to moving out. I would also insist that she do a walkthrough with you before you're officially out, and tell you what may be billable or taken from your deposit.
So in that sense, you're pretty well protected and not likely to be immediately homeless if she doesn't take it well. But, why does she need to know? If you see her often and misgendering makes you extremely dysphoric, then I could see how it would be important to tell her. But in my experience, I've had very little interaction with all of my landlords post lease signing. I either pay online, or drop a check in the box. No need to talk to anyone. I can e-mail about maintenance issues. I transitioned in the middle of my last lease and never told anyone. Nobody cared that a new name was on my checks as long as my rent got paid. When I moved to a new place, I provided the new property manager with a copy of my name change order so she asked for my old name when she called for a reference.
I think it just really depends. If you see value in her knowing, either in that it makes you feel better or it maintains a positive relationship, then tell her. But at this point, since it's a relatively unknown factor I'm not sure I would rock the boat needlessly if I were in your position.
