Translation:The girl needs to get up tomorrow at seven.
As dictation this is tricky - the unstressed е at the end of девочке will sound much like и; I had interpreted this as Девочки, нужно встать... = Girls, [we/you] need to get tomorrow at 7.
Only if you wanted to say "The girls need to..." Not if you address them directly, as in, "Girls, you need to..."
well, there is a trick in Russian pronunciation. The accent falls only on one syllable, one vowel, so it will not change but all the others will sound different. o = a, e = и
This is not a very good sentence. "Завтра девочке нужно встать в семь" sounds much more natural. Девочке нужно завтра встать в семь, Девочке завтра нужно встать в семь are also ok. But not the one given in the exercise.
Ну́жен (ну́жно, нужна́, ну́жно) is a "state" that is imposed on a dative noun that experiences that state. If the required thing is some object, it is the grammatical subject of the sentence (e.g., Мне нужна лопата). The form of нужен will then reflect the gender/number of the noun. For verb infinitives, it is just нужно.
To give you a glimpse of the bigger picture, Russian has a number of "experiences" that work that way. In English the verb "seem" behaves similarly.
- telling age: Мне 25 лет
- telling that someone is feeling cold/hot/warm/well/unwell, someone is scared, interested: Мне холодно / жарко / страшно/ интересно etc.
- нужно, надо, необходимо
- a number of verbs : казаться ("seem"), нравиться (usually translated as "like"), хватать ("to be enough"), не доставать ("to not be enough"), приходиться ("to have to", as in to be forced to due to circumstances), удаваться ("to manage to" do something).
- some reflexive verbs that express your inclination to do something or how well you are doing at the moment: хотеться, спаться, работаться
A note: verbs that end in -ся, the so called reflexive verbs behave as if the action were performed on the subject itself (ся used to be a clitic form of себя "oneself, itself"). They cannot have a direct Accusative object, with the exception of бояться "to be afraid" (which can). If these is any "object", it must be in some other case.