Visa for Baby?

We have been residents (on work visas) in the UK for 6 years and are currently applying for permanent residency. When I went through immigration I was informed that I need to have a separate visa for my 4 month old baby (who was born in the UK but has a US passport). Does anyone have experience with this? Do you know how to apply for this kind of visa and how long it takes?

I thought kids born in the UK to people who have ILR are eligible for British nationality.  But someone else may know better! 

don't know about the visa question, but....according to the IND website, if you get your ILR or become a UK citizen before your child is 18 years old, the child is entitled to become registered as a British citizen because he/she was born in the UK. 

18. If a child does not become a British citizen at birth, he or she may be entitled to registration as a British citizen later. This will happen if either parent becomes a British citizen or legally settles here before the child is 18; or if the child stays here until age 10. If the child is not entitled to registration, the Home Secretary may decide to allow registration. There are more details in leaflet BN11 which you can get from the address in paragraph 19.

edit- just read expat's post- I was assuming since you said you were applying for 'permanent residency' that you don't have your ILR yet- if you do, then your child is already a british citizen.  If you don't, your child is not british, but is able to become a british citizen once you do get ILR, like I said above.