You needn't worry unduly. I am a music writer, and I have been to The Academy numerous times, and never seen any trouble of any kind. The gigs are supervised - the venue is University premises, so it's all supervised.
Just a word - Academy One is an individual one-storey building, part of the Universtiy Campus. Academy 2 and 3 are part of the main Students' Union Building, on the second and third floors respectively, and there are often separate gis at all three on the same night, so make sure you go to the right one - folllowing the crowd may get you lost! Both buildings are 30 seconds' walk apart, on a main road - oxford Road - so you needn'w worry about your daughter emerging into a dark dingly place.
She will be fine.