Tier 2 visa - baby born in UK but getting visa outside UK

[Ray47]

I have a tier 2 General visa, have had a baby this year but did not realise before today I would need to get her a UK visa to travel. We are travelling to the US in a very short time frame, and will not be able to get the baby's visa before we leave the UK. We will go through the visa application process in the US (where we're from), via priority processing.
I want to make sure I have everything I need and that the application form is absolutely correct, to prevent any delays.
Does anyone have any experience with this? I am completing the 'outside UK' application on the gov.uk site but because the baby was born in the UK is there anything else I might need to provide? The site/application doesn't seem to account for this scenario. Are there any pitfalls to avoid?

[iworker]

that is fine.
take following docs with u.
3 month bank statement showing £630+ min balance.
original birth certificate,
your and your partner visa.
I think u cant apply for priority processing visa from outside uk, but i maybe wrong.

[gag285]

I have a question on similar lines - I recently applied for my daughter's birth registration at the Indian High Commission and waiting for the process completion post which I would apply for her Indian passport. Meanwhile, I was looking at the UKVI's online visa application system and for PBS Dependent Child, the system seems to work without the need of a passport. ( It has the option that says I have never had a passport because I was born in the UK). All it lists as mandatory documents are -
1. Photo
2. UK Birth Certificate
3. Maintenance proof.

I called the UKVI helpline to confirm this and they said, if the online system allows it, it's fine. With numerous examples of UKVI helpline soliciting inaccurate advice, I am unsure of going ahead with an application without her passport. The only benefit it serves is time-saving with parallel documentation processing

Is there anyone who knows or has done so in past?

[Ray47]

that is fine.
take following docs with u.
3 month bank statement showing £630+ min balance.
original birth certificate,
your and your partner visa.
I think u cant apply for priority processing visa from outside uk, but i maybe wrong.

Thank you! I haven't been able to find any official information online about this scenario, so it is helpful to know that it should work - I've been very worried. I was hoping to see if anyone had gone through this same scenario successfully...?
There is a priority processing service offered by VFS in the US, though no information about processing times. Hopefully they are quick!