For this example "This girl is my sister.": writing dash is mandatory, but for regular speech does not have effect.
Note: For "i am a teacher", you can write "я учитель" without dash.
Dash is very difficult punctuation symbol. For beginner language level is not mandatory full understanding.
I recall reading in another discussion that the em-dash "—" is used when the subject NOUN is the same person/thing as the predicate that follows it. (Predicates modify, quantify, qualify, describe, etc. the subject of the sentence.) That is case in the present sentence,
«Эта девочка — моя сестра».
In the example given by 3g0r, you don't need the dash for «я учитель», because "I" = я is not a noun, it's just a pronoun. But in «Дима — учитель» the em-dash is necessary because "Dima" is a noun.
This needs some verification, but the person making the comment said that he'd consulted with some native Russians about it.
I feel that you do that only this way: She's dumb, he's dumb, etc. not with nouns like The house's big. The reason behind it may be that you could say The house's domain, which would mean The domain of the house. The house's big would be something like the big of the house, which would sound dumb and illogical and wrong.
Native speaker/Someone who knows may confirm or tell you more. I just give a hint of what I feel is the problem with your abbreviation.
You can do this with singular nouns: "The dog's outside." "This man's my father." "Russian's my favorite language." You can do it with plural nouns also, but only in spoken language. To do it in writing would be understood, but is not standard English: "The dogs're in the kennel." <-- never write something like this!