short answer - yes you can use the だ copula in that way, and your alternatives are not correct.
long answer - yes the だ is declarative and you are correct to assume it would be incorrect. however, there are several factors that allow you to use it in a question.
The main reason is that アリスはどこだ makes no sense as declarative sentence.
'Alice is where!'
And since どこ functions grammatically as a noun here, it is proper to attach the だ. We are forced to read it as a question.
In regards to your alternatives アリスはどこの and アリスはどこだの, you are correct in that の can be used as a question marker. It is softer and a little bit more feminine than か. (But I do hear men use it as well sometimes) however it can't be used like this. You might see アリスはどこなの？But I think almost everyone in a casual situation would simply shorten it all the way down to アリスはどこ？Usually the の as a question marker can only be directly slapped onto the end of a verb. Not exactly sure why but I just know it can't be used like you ask. Let me give you some examples to help:
今日帰るの？
Will you go home today?
あれは．．．何なの？！？
That...What is that?!?
ジョンのかばん？
lit: John's bag?
ナットは本当に食べれるの？
Can you really eat natto?
Just as an interesting sidenote, I live on the west coast of Japan in an area called Shonai. If you saw the Academy Award winner for best foreign film a couple years back 'Departures,' it was also in Shonai. In 庄内弁 (Shonai accent) のis used instead of the な gobi and so we actually say ...だの all the time here. It sounds so funny that shonaiben is the laughingstock of japanese dialects.
今日はまた雨だの。
Today it will be rain again, won't it...
short answer - yes you can
short answer - yes you can use the だ copula in that way, and your alternatives are not correct.
long answer - yes the だ is declarative and you are correct to assume it would be incorrect. however, there are several factors that allow you to use it in a question.
The main reason is that アリスはどこだ makes no sense as declarative sentence.
'Alice is where!'
And since どこ functions grammatically as a noun here, it is proper to attach the だ. We are forced to read it as a question.
In regards to your alternatives アリスはどこの and アリスはどこだの, you are correct in that の can be used as a question marker. It is softer and a little bit more feminine than か. (But I do hear men use it as well sometimes) however it can't be used like this. You might see アリスはどこなの？But I think almost everyone in a casual situation would simply shorten it all the way down to アリスはどこ？Usually the の as a question marker can only be directly slapped onto the end of a verb. Not exactly sure why but I just know it can't be used like you ask. Let me give you some examples to help:
今日帰るの？
Will you go home today?
あれは．．．何なの？！？
That...What is that?!?
ジョンのかばん？
lit: John's bag?
ナットは本当に食べれるの？
Can you really eat natto?
Just as an interesting sidenote, I live on the west coast of Japan in an area called Shonai. If you saw the Academy Award winner for best foreign film a couple years back 'Departures,' it was also in Shonai. In 庄内弁 (Shonai accent) のis used instead of the な gobi and so we actually say ...だの all the time here. It sounds so funny that shonaiben is the laughingstock of japanese dialects.
今日はまた雨だの。
Today it will be rain again, won't it...