You simply must IGNORE the whining, and turn your face away. Tell her you can't hear her when she whines.
Se must get the hang of being social, for all our sakes! If there's one thing worse than having your own child whining and whinging, it's having to listen to someone else's kids whining and whinging.
So, it's best it's nipped in the bud by you with love, before some stranger has a go and who might teach her harshly.
You might want to teach her some sign language also. We did this and our DC could sign what they wanted when they were preverbal.
Persistence and good humour are required to teach her to ask using her words.
Ignore behaviour you don't want, (turn your face away, and then look back and say matter of factly, DD I can't hear you when you screech like that, use your lovely voice and your words, look away again if she kicks off and start humming, repeat as necessary, (whispering 'I can't hear you' is also good, as it changes the volume)) and praise praise praise when she starts to get the hang of communicating well.