ILR and FLR(M) for respectives spouses at the same time?

I have a query regarding both mine and my wife's application. I would be applying for my ILR soon after completing 5 years on Tier1. Now my wife only joined me in the UK about 18 months ago and obviously her visa expiry date is the same as mine and she isn't eligible for ILR yet. I want to apply through a PEO to save time.
Now is it possible for both of us to apply together i.e. me for my ILR and she for her FLR (M) (I assume) on a single appointment at the PEO with her being the dependent?

If you are applying for ilr as a PBS migrant then your wife needs to extend her leave on the PBS dependent form not FLR(m). She would need a separate appointment after yours. If your application is not decided on the day she should apply by post unless she has time to make another appointment.

Thanks for the clarification Greenie.

My wife is expecting a the moment and is due to give birth a couple of months before my ILR is due. Now with regards to the baby, should I wait till and I get my ILR and then apply for a British Passport for the baby or will the baby apply with my wife when she extends her visa as PBS Dependent?

Baby will not need to apply for leave to remain, unless travelling.