Lip-syncing to a CD (if she has one) is good because you can do multiple takes from different angles, in different costumes, different lighting, etc. to cut together for that "music video" look. BUT, for an audition reel she probably doesn't NEED or want all that variety. Just a straight-forward shoot with only a couple of camera changes, if any. Assuming she's actually going to be singing, get the BEST audio you can manage, then feed half of it into the camera (mainly as a reference because of the compression, although it may be sufficient for an audition tape), and the other half into an external recorder -- CD, DVD, Mini-Disc or computer recording a WAV file at least -- in other words, something you can work with later to importing into your editing equipment if you need it.
DO NOT USE THE CAMERA MIC. Depending on her "style" she could "croon" into an old-style 50's chrome stand mic; she could rock into a contemporary stand or hendheld; she could be "in a studio" with headphones, singing thru a pop screen into a fancy condenser diaphragm or ribbon; or you can simply hang the best mic you have just above her (out of frame) and let her get the best take she can, without any visible miking, to just concentrate on her "look". The point is to do what you have to (including slight processing, although I usually like to get it "raw" as a baseline version) to get the BEST audio you can achieve, inline with her desired performance "look".
One tip from me as a union performer, the people getting this audition video will most likely know in the first 30 seconds whether she's right for them, and they won't watch any further. So you shouldn't plan or execute a full-blown "video" with lots of "extras" or fancy shots or lighting. It's easy to get carried away and want to do your best "stuff". Remember it's not YOU they're auditioning.
It also helps to Fade up into a title card at the top, to "slate" the thing, giving her name, union affiliation (if any) and contact info. Fade to black just before the video starts and/or make it a seperate track on the finished DVD, so they can bypass it to jump directly to her if they want to show her to someone else.
