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Whatsapp is horrible, fake, unnatural and completely irreplaceable...
Change your settings so people can't see your login time, and you can't see theirs. Believe me, it's saves a lot of stress in the long run.
If you'd met her in a bar, naturally, in the olden days, you wouldn't have a clue. Your watching her logon times is like having a friend following her and saying 'well she went went to work today, she went to the shops, her phones working because I could look through her window and see her on it' - it's odd and it's understandable but it's obsessive.
Turn it off, send her a message, casual and breezy, funny, about something you talked about.
You see posts on here about men who get all possessive and pissy about women being on OD sites and how dare they, and the justified response that it's none of the man's business.
She's a surgeon. She's very intelligent, and very stressed, and very busy. She's possibly too good for you. And isn't that what we all want, someone who is too good for us but doesn't know it, and thinks the same of us?
Send a casual text about something OTHER THAN her failure to be in touch. Be cool. Be calm. Be friendly. Don't stalk her. Give her a chance to see you're great and contact her when she wants to.
If she doesn't, then she doesn't. Her loss.
But please, mate, turn off the timestamp.