My letter saying I qualified came pretty quickly (probably about a week I would say) but I had been warned it could take nearer a month when I rang to check they had received the forms ok.
EmmaLou - they only pay 2 weekly or monthly depending on what you requested so I bet you just missed a payment with the timing of sending your letter, I wouldn't worry too much, the first payment will catch you up, mne took nearly a month to come through (even though I'd asked for 2 weekly payments) but I got the back pay in the first one.