Hi loll01,
As long as you have done everything within the timescale dictated by DWP, your daughter's DLA will continue in payment until 4 weeks after the PIP decision, whatever that may be. It is up to you whether to contact the DWP to try and speed up the process. As you say, you do run the risk of losing several months of payment if the PIP decision were not favourable.
Whether the claimant needs a face2face assessment depends on whether the HCP believes there is enough information to make a decision without.
Nothing on this board constitutes legal advice - always consult a professional about specific problems