There are plenty of professional MTFs out there that prove him otherwise. Yes, it may be harder for those of us who are not established, but I know transwomen that started there careers after the fact too. Being trans isn't easy and you will face discrimination in this world in some form, but it doesn't mean you are destined for a life of unemployment. I've been able to get hired despite my situation and there are plenty others to. Again, it's harder than it should be, but it doesn't mean you can't find something. I believe my job search has been much much harder than it should be, but I have gotten passed this in the past and will be able to do the same again. Don't give up hope and work hard to secure something.
As for mentinining that you are trans on your application, something tells me that its not the best idea. If it's not related to your job performance, it may be best to refrain from talking about it. Having said that, take my advice with a grain of salt because I'm currently looking for work myself and don't have all the answers.