Can I prove my type of UK citizenship with my passport?

I have full British citizenship.

My infant daughter was born abroad and is therefore British by descent – I have passed my citizenship to her, but she cannot pass it on (unless she goes through the naturalisation process also).

My question is: Can my type of British citizenship be determined directly from my passport, for instance from the passport number or another code?

If so, the passport and her identity card would prove she is a British citizen. (If not, the passport would only prove I am British by descent, in which case she would need her own passport to prove her citizenship).