British Expats - Processing times/documents for first child passport born overseas?

HI all,

Apologies if this is not the correct place for this query. First time poster.

I'm a UK national, moved to the US 6 years ago, married my wife (US national) in 2017. Our daughter was born mid-pandemic last year, I'm now looking to get my daughter's UK passport application filed, but would like to get the group's take on 2 things:

1) Does anyone have a rough idea as to current processing times for first time child passport applications from overseas? We are hoping to travel to the UK in December to see my family (travel restrictions permitting); while we wouldn't necessarily need to have her UK passport issued in order for us to travel, we would need to have my and my wife's passports, which I understand I will have to submit as part of my daughter's passport application. Is 3-4 months a reasonable time to expect to receive back the the original documents for such an application?

2) In terms of the documentation we are planning to submit, please see the list below. Is there anything that we are missing that jumps out at people?

Daughter's original birth certificate
Daughter's original US passport
Full colour copy of every page of daughter's US passport
Daughter's original US social security card
My original UK passport (valid at time of conception - lovely phrase on the Govt website there)
My wife's original US passport (valid at time of conception)
Our original marriage certificate
My original birth certificate
My Mum and Dad's original birth certificate (both UK nationals), as both my wife and I were born after 1983
My Mum and Dad's original marriage certificate
Cover letter explaining that since my wife's nationality has no bearing on my daughter's UK citizenship, we have not included birth certificates for my wife's parents, nor their marriage certificate

Thank you in advance for any advice and guidance