Emergency first passport for infant

Hoping someone can help with this query. I am looking to go away on the 10th Jan with my 3 month old daughter. Problem is I completely forgot about getting her a passport before now. I haven't booked the holiday yet and don't want to do so unless I know we can go. So my question is, is it possible to be issued with a passport on such sort notice if I go into the passport office? I've checked their website and they issue them for urgent travel. Obviously this travel is not urgent so I'm wondering if they will issue an emergency passport for a holiday (i'm happy to pay an extra fee for this). Does anyone know if this can/can't be done? (I can't go away any later in January so waiting for passport express is not an option). Thanks.

As far as I'm aware they will issue a passport within a day or two if you have proof of travel (i.e. airline tickets)

As previous poster stated they will normally issue an emergency passport if you show the flight tickets and pay a fee. I've just travelled on an emergency passport myself as they rejected my photos two times but there was no fee in my case.