Yes, as soon as you can, I think you need a copy of the birth certificate for one. Ring or ask online for the forms you need tomorrow and get them all filled in asap, so that when you get certificate/proof of her existence you can just post. I think both will backdate up to 3 months but of course the sooner you apply the sooner you get the cash.
I've heard of people adding subsequent dcs through online application but not sure how it works.
To claim CTC you can either phone or write. To claim child benefit you need to either phone for a claim form or download from their site and send it with birth certificate. They will only backdate for three months. At the moment ie this last week, they are not answering the phone!! v v frustrating.
you can inform them of additional children online but will need to send the birth certificate through as well and do it as soon as possible as sometimes it takes a few months for them to process although it will be backdated.