Yup! From my understanding it's perfectly acceptable and even more common in spoken French but "avez-vous" would be more formal and used in writing. In French the phrase "est-ce que" is often used before a sentence to signify that a question is being asked so I believe even "Est-ce que vous avez une fille?" would be an appropriate way to ask this question.
You have a daughter? would also be the most natural way to ask the question in an incredulous manner. Either putting the emphasis on 'you' to make it clear that it is difficult to understand that you personally have a daughter or letting the tone and volume rise throughout to express general surprise in a less accusatory manner.
It seems to me I read a discussion some time ago about this in reference to asking if someone spoke English. There was some debate on whether to say "Parlez-vous Anglais" or "Vous parlez le anglais?" and I remember someone who was a native french speaker saying that either is correct, but the inflection of the voice carried the intent of the question. Is this not a correct assessment?
not sure if the sound file still sounds the same as it did when you posted your comment, but students should note that the sound of french sentences (intonation, rhythm, speaker's voice) are sometimes different from english: https://en.wikipedia.org/wiki/Intonation_(linguistics)#Intonation_in_French
for example, the question "avez-vous une fille" rises at the end while "est-ce que vous avez une fille" falls at the end.
If you think as English it is kinda funny yes. But didnt you notice the translation of the rich men is 'les hommes riches' It is another point that do not match with English. And here is the point what makes it a question is the pronounciation. If you listen carefully you will notice the pronounciation to the end is high. Espeacially in 'fille'
You have to listen to how the words sound when they are strung together. Usually, the z in avez is silent, but since it is followed by a vowel sounds, in this case "une", it is pronounced. So it sounds like, "Vooz avezoon feeyuh."
With avec, the words will not flow together. So, it sounds like "Vooz avek oon feeyuh."
In general, "avez" will be pronounced like "avay". The z will only be pronounced if there is a word beginning with a vowel after avez. "Avec" will always be pronounced like "avek". I hope this clears things up.
Assuming we're talking about a complete sentence, it would require a verb. 'Avoir' is indeed a verb, conjugated with the present form for 'vous', which yields 'avez'. On the other hand, 'vous avec une fille' is not a correct sentence. It means "you with a daughter" and lacks a verb... Hope this helps on more than just the sound, but also the logic which could help you figure out which word is being used.
As explained, vous is formal, but it's also plural. So the questioner could be asking a couple (say you meet a couple at a party and you chat about your kids.) In which case, vous avez covers both being formal and speaking to two (of more, depending on context and question) people. HTH