That has happened to me twice lately, and I have assumed they didn't spot it, so, later in the evening, I posted again. ''Hope you had a lovely birthday.' (Coz I didn't know if they had seen my post and didn't want them to think I had not messaged them a birthday greeting...)
Response.... 'yay thanks tippz it's been fab!' 
Just post again, 'I hope your DD had a good birthday.'
Your friend may be stewing coz she thinks you haven't wished her DD a happy birthday LOL. Just remember, some people get 50-100+ birthday messages, (on FB) and it is easy to overlook one or two.
Oh and I agree with the posters saying do not message her to say 'why did you not like my post?!'
Just say 'hope your DD had a fab day!!!' You could even put (at the end of that message,) - 'hopefully, my birthday greeting for her from yesterday got through!' with a big grin > 
Chances are high she didn't spot it, or did spot it and didn't realise she hadn't liked it!
The posters taking the piss out of the OP, and bashing her, are being unfair BTW; some people stress about stuff that YOU wouldn't stress about. That doesn't make you better than them. So quit mocking, and get off your high horse. 