I am shorter than you are. Do I think I would have had more success with dating had I been taller? Yes. Have I had difficulties with dating? No. Height is a factor, certainly more relevant in terms of how much action you might get, but it is only one factor. And in many ways it is only as much of an issue as you make it.
My advice is:
1. Don't appear desperate. You probably don't realize you're doing it but a lot of guys come across as desperate and it is a turn off.
2. Don't be the guy who projects an image of himself as empty or incomplete. When you enter a relationship with someone you are looking for someone to enrich your life, not some black hole.
3. Online dating is good, but it is only one way of meeting people. You don't necessarily have to be looking for someone, often you will find someone when you are not looking (and not coming across as desperate).
4. Do not list your height for online dating. I don't. I am certain things worked better when I didn't list my height than when I did.
5. Don't go looking for short women or restrict yourself to shorter women. In my experience, shorter women are looking for taller men too, in fact, many really wanted taller men. If you limit your pool by height, you're not playing it smart, you are reducing the chances of finding someone. I have dated women who were a lot taller than me, and those that were a bit taller. It wasn't a big issue because I never made it one.
6. Being a doctor does not trump being short. There are enough doctors who are taller than you to mean you don't have the competitive edge! I am sure that being a doctor might have some attraction to some women
7. If women say you're nice, a good guy, or wonderful, it's usually (but not always) the kiss of death. It means they're not into you in that way. If you get this a lot, you need to think hard about what it is you are doing that means women see you as a friend, or worse still a lovable pet, but cannot see you as a romantic partner or sexual being.
8. I know it is hard to tell on an internet forum but you guys come across as not really believing would actually be interested in having a relationship with you. If you can't convince yourself, how do you persuade anyone else? Persistence is important, sometimes a 'no' isn't really a no. Women like to feel attractive, wanted, pursued. I can think of at least one ex who initially rejected my advances eventually acquiesced because I wouldn't take no for an answer. You need to be able to judge the situation, and not be some creepy stalker - there can be a fine line but its there.
9. Finally what barriers might you be putting up? This might seem counterintuitive, but if you have not had much or any luck with women, it gets harder as you get older, and whilst a relationship might be something you crave, it might also be a source of fear. It is possible that on the one hand you put yourself out there, convincing yourself your trying, on the other hand you might inadvertently be pulling away from any chance of a relationship.