This girl is actually expressing the concept of: Must do something. In Japanese grammar you can use two basic grammars to achieve this.
But remember that we are not talking about giving orders (which has a complete independent form in Japanese grammar).
Quite direct and informal approach
When you talk with a friend, this is actually the easiest way to say: Must do something, intended as something needed, some sort of task to do.
(Verb:ない-Form)と ==> Must/Have to...
Or, extended...
(Verb:ない-Form)といけません ==> Must/Have to...
Here are some examples:
1) 明{あし}日{た}は試{し}験{けん}があるね。勉{べん}強{きょう}しないと! => Tomorrow I have a test. I gotta study!
2) ごめん、スーパーへ行{い}かないと〜今{きょ}日{う}は用{よう}事{じ}があるから、遊{あそ}びはちょっとだめ! =>
Sorry, I have to go to the supermarket... Today I have errands so, I cannot play with you!
3) 映{えい}画{が}って?やだよ!まだ宿{しゅく}題{だい}をしないと! =>
What? A movie? That's impossible! You still have to finish homeworks!
4) まだ下{へ}手{た}なので、もっと練{れん}習{しゅう}しないと〜 => 'Cause I am still bad at it, I must train more...
Saying it a little bit more formally (but not that much)
When you are not with friends but with adults or superiors or in a context new to you, you should use the following form:
(Verb:ない-Form->{drop い})ければなりません ==> Must/Have to...
Here are some examples:
1) ああ、明{あし}日{た}は学{がっ}校{こう}へ行{い}かなければなりません! => Mmm, tomorrow I have to go to school.
2) 昨{き}日{のう}は試{し}験{けん}があったので、京{きょう}都{と}へ行{い}かなければなりませんでした。 =>
Yesterday I had a test, so I had to go to Kyoto.
3) この薬{くすり}を飲{の}まなければなりませんから、その薬{くすり}まで飲{よ}めない! =>
I must take this medicine, so I cannot that one too.
4) 強{つよ}くなりたいんですね、じゃたくさん食{た}べなければならないね〜 =>
So you want power... you must eat a lot...
Another way...
There is another way to express this. It is actually used by kids and girls and it is encountered very often in spoken language (believe me, they use it a lot). It is the following:
(Verb:ない-Form->{drop い})きゃ ==> Must/Have to...
Here are some examples:
1) ああ、難{むずか}しいよ!もっとまじめにしなきゃ〜 ==>
Mmm, this is difficult! I must go for it more seriously...
2) あの電{でん}車{しゃ}に乗{の}らなきゃ! ==> I must get on that train.
3) 車{くるま}はだめだよ!歩{ある}かなきゃ! ==> Car is not allowed! You must go by foot.
About your question...
The girl is saying this:
素{す}晴{ば}らしい。ドイツ語{ご}も勉{べん}強{きょう}しないとですね。 => Wonderful. I have to study German too.
From the context you provided it might sound quite sarcastic as well.
This should help you in future when you encounter other similar situations...