Submitting parents naturalization and child’s registration at the same time

[justanothername]

Hello,

Me and my husband are eligible for citizenship next month following one year on ILR. My daughter was born outside UK and has ILR for the past year and from what I read is eligible for citizenship via registration.
My question is whether the applications are processed separately or together? I see Registration applications being processed fairly quickly but Not Naturalization. The reason I ask is she is scheduled for a school trip to US mid February and will need British passport before she can travel (Indian passport needs visa and the wait times are ridiculous and I won’t be able to get visa by February). My son got his citizenship within six weeks earlier this year as he was born in the UK so I am wondering if my daughters registration will follow similar timelines or if us submitting the naturalisation at the same time affect the timeline.
We’d have to submit our naturalization regardless but I am more worried about the timelines.
Appreciate if people with similar cases can share their experience. Thanks!