Don't worry,you still have time to get your new QID.
for your childs sponsorship no need for NOC since she was born here in Qatar.requirements are as follows;
1. Copy of your valid QID and your wife.
2. Babys passport
3. marriage certificate.
4. babys ID picture-white background
5. Copy of her birth certificate.
6. blood typing-you can see it at babys green card from Hamad (make a xerox copy of it)if not you need to have her blood typing at any laboratory clinic.
7.family visa form signed by you as her sponsor- you can get it at the typing office infront of building 2 of immigration.

Next step is at building 2. go to the man at the reception and show him the documents.He will give you no. and will ask you to go to the capt. at the end for verification and approval.if okay ,sit down and wait for your no. to be called.Visa will be issued right away free of charge.