Which is the correct sentence?

1. Is right.

1. Did the girl ask, "When is dessert"?

2. Did the girl ask, 'When is dessert?'?"

Did you actually intend #2, as I've underlined, to be like it is, MsTan?

We've really got two questions here.
1. In the US double quotation marks are usually used (like T's question 1). In the UK apparently either single or, rarely, double quotation marks are standard (ala most of T's question 2).

2. However, as JTT points out (I think this is what he is pointing out), the double quotes at the end of question 2 have no obvious reason to be there. It does seem to me that since the girl's quote is a question, and the sentence as a whole asks a different question but is not itself a quote, that it should in fact end: ...dessert?'? strange though that looks.

Yes, JTT, I think the second sentence is correct. I want to confirm that I'm right.

Monterey Jack thinks so too although the two question marks appear unusual in writing.

I'm not sure Monterey Jack does agree about that.

The problem isn't the two question marks, it's the two sets of quotation marks at the end of the sentence. There is only one quotation in the sentence, so there should only be one set of quotation marks, and I think they should be double quotation marks.

I think single quotation marks would only be used within double quotation marks to indicate a quotation within a quotation. For instance:

I said to John, "Do you remember when Bob asked me, 'Do you ski?'?"

I think the sentence should read:

Did the girl ask, "When is dessert?"?

That isn't either choice 1 or 2. Perhaps you need choice 3.

Thanks, Firefly.

I don't know what the other native speakers think it should be.

Mo, Monterey Jack doesn't think sentence 2 is correct. If you left off the double quotation marks (where did they come from?) at the end, it would be.

There is also a difference in usage playing into this question. Firefly is right that in the States a quotation is set off in double quotation marks at either end, and a quotation within a quotation is set in between single quotation marks. (though we don't have a quote within a quote in the example). However in the UK a quotation is usually set inside SINGLE quotation marks, and I have no idea how they show a quotation within a quotation.

So, EITHER of these would be correct, depending on how Anglophiliac you are:

Did the girl ask, "When is dessert?"?

or

Did the girl ask, 'When is dessert?'?

Is it possible that the double quotation marks (at the end of choice 2) were a typo? They obviously don't belong there.

I agree with the two choices Monterey Jack has given. But neither of those are the same as choice 2.

I think we are back to needing a choice 3.

My guess is the double quotes are a typo, yes, however we don't know that for sure, so it's best I think to nail down that they shouldn't be there.

Thanks to all the members who have responded to my query.