Being trans for me really didn't change anything except it allowed me to be me. The only time I faced discrimination, I think, is when I made being trans a problem by saying things like, "I want to work somewhere that will accept me." I really don't think the few employers I said that to liked that. I also didn't present as myself which I think exacerbated the issue.
My current job, while the medical coverage is out-of-pocket expensive if you're not a straight male, did hire me. I went in for my interview dressed professionally as any woman would and presented myself in a knowledgeable manner in my field. I mentioned my trans based research but as a point of accomplishment and a demonstration of how I want to help people. In the end, I think being trans HELPED me get my job.
It also kept me from getting fired at my last. I was so angry as a guy, I was starting to become a problem for clients.
The set of job interviews I'm on now started with them reaching out to me via an e-mail address from a 2008 interview I had. So I had to start off with, "Great! I'd love to talk to you about a position! Only it's not [REDACTED] anymore. It's Paige!" and gave them my new e-mail address. Recruiter switched over without comment. Best relationship with a recruiter I ever had too. Even got a gift basket.

Anyway, I had one interview a week ago Friday and two more this coming Tuesday and Wednesday for four possible positions. My point: being trans hasn't hurt my career prospects at all now that I don't let it get me down or drip with fear over being trans. If I don't get a new job out of all this, I'm sure it won't have anything to do with being trans. In fact I'm soooooooooo close at landing my dream job right now!
Joanna, from the field I can say if your JavaScript and CSS is current you're going to be fine on the web. Just be yourself and knowledgeable in the interviews. Be positive. Encourage your interviewers to think, "I want to be around this person for 40 hours a week. She seems cool and knowledgeable." <-- This is also why they would hire
you over anyone else. I'm routinely finding that being trans just isn't a issue unless I made it one by showing off some of the extra baggage I used to have.
I know my experience is anecdotal, and I know the statistics for trans people landing jobs, but I do believe the stats don't have so much to do with the core of being trans but instead their reason for being is the baggage like that I used to let show. So, being positive and celebrating yourself is certainly worth a try.
Best of luck to you! Go get em'!