As of this moment there is no calllog or callhistory api, to just extract all calllogs in one shot.
Another option is to listen for calls. You would record as a call gets made and store information about it. The app obviously have to be open when the call is made, to record it.
So basically you would have to write the history yourself.
If this interests you,
you need a class that has a slot:
public slots:
void callUpdated(const bb::system::phone::Call &call);
you then connect the slot to retrieve updates about calls:
CallListener *callListener = new CallListener();
bb::system::phone::Phone *m_phone = new bb::system::phone::Phone();
QObject::connect(m_phone,SIGNAL(callUpdated(bb::system::phone::Call)),callListener,SLOT(callUpdated(bb::system::phone::Call)));
I see you say you are new to BB, the above code is just a brief example to point you in the right direction. If the logic does interest you, write a comment and ill adjust my answer with more details.
Hope this helps.