Is your child British? Assuming so, hope this will help. I just got ILR last week, and have a British child, so just went back and reviewed my application and I was asked no questions about my child. I was asked about my spouse and a yes/no question if we have children, but nothing else in the application about my child. In the free text question about reasons for wanting to remain, in the 'Documents' section, I mentioned my child, and then in my document pack to support this I included their birth certificate, passport photo page, and a few pages from their red book.
I'm no expert, but this was my experience a week ago! Good luck!!