You can definately claim for depression/pnd etc. You need to get a sick note from your doctor and send that in together with claim forms which you can get from the benefits agency. You should get at least 6 months before a benefits agency doctor examines you, as misdee said. However, tbh and IMO the benefits agency aren't really going to crack down on pnd, just because they should know that its normally a temporary condition-its people with long term sickness (or potential to become so) eg back problems, that they mainly go for. So I would be suprised if you were examined before you had claimed for about a year at minimum.
However, you do need to have paid enough NI contributions to claim. If you have worked full time for the last 3 years (ex maternity leave prior to baby being born, etc) , and then claimed child benefit, I think you'll be ok.
If you are on a very low income and your partner (if you have one) does not work + 24 hours, you might get Income Support even if you haven't paid enough NI contributions.
It can be worth claiming Income Support even if you do get Incapacity Benefit as you might get a small top up, this entitles you to free prescriptions etc.
Also, you might be entitled to some other beenfits eg Housing and Council Tax benefit, Disability Living ALlowance (possibly-quite hard to get).
I assume that you know about Child Tax Credit and Working Tax Credit and are claiming these if eligible?
HTH. A CAB or similar can go through all of this with you and check that you are getting all the benefits you are entitled to. there is also a number that you can ring to find out whether you have paid enough contributions-they should have it for your part of the country.