Citizenship for child when settled from a GTV

Dear Forum,

I am a Tunisian citizen who recently received his ILR after 3 years of global talent visa. My kid was born 3 years ago in the UK and has been since on a dependent visa. Can I apply for her to become a British citizen after I became settled? knowing her mother is also a Tunisian citizen on a dependent visa who will qualify for ILR two years from now.
Moreover, my wife is pregnant and will give birth soon, would my son be registered automatically as a British citizen?

Many thanks

I believe they are both eligible for citizenship. Best to check with an immigration lawyer.