MN 1 application pending and travelling abroad

Hi All,
Please anyone can advice,my uk born daughter MN 1 is pending and she need to travel with her mum next week,she has a paksitani passport at the moment,I know there will be issue for her when travelling back to uk, as by the time she will come back her MN 1 application will be decided and can apply for british passport,
My question is can I apply for her british passport here in uk using fast track service,so I can go back to my home country pakistan along with her passport to bring my daughter back to uk? Because if she apply for passport abroad it will take 6 months to process it.

Many thanks