Ok, but 'meet' is face-to-face and get to know can also be on msn..
Anyway, if you think meet is better then I would suggest the sentence as follows:
Hi, I am a doctor and I would like to meet you. You are very beautiful. What do you think about meeting?
(in Turkish you say 'seninle tanismak', but in English you don't translate the 'with you', it is already implied in 'meeting' )
Hmm sorry, I think 'what do you think about meeting' is about an opinion of meeting someone, not really that you want to meet someone.. My mind is a bit confused now, let's ask kafetzou how to translate this properly into English..
Oops - I just saw your message - sorry! Yes, Chantal, you're right that "what do you think about" is wrong. "How about getting together?" would be better.