As far as I can tell, such a thing doesn't exist--I have never seen a multilingual Danish dictionary that had the pronunciation of the Danish words listed. You can find Danish-only dictionaries with the pronunciation listed, and you can find multilingual Danish dictionaries with the pronunciation of the words in the other
language listed, but I've yet to see anything which combines the two (well, there was this one rather thin and not very comprehensive Langenscheidt dictionary with the words in some bizarre and necessarily doomed attempt to transliterated the words into English, but that would probably be more hindrance that help, as Danish is very much NOT transliterateable into English). That said, you can always consult one source for meaning and another for pronunciation.
Your best bet is Den Røde Gyldendal Tysk-Dank Ordbog
. Bear in mind, though, that you can get three different versions of this: Tysk<->Dansk, Tysk->Dansk or Dansk->Tysk. (I'm pretty sure the one linked to above contains both directions, judging by the 153,000 entries listed, whereas my Tysk->Dansk only version has just 80,000). You can find this in pretty much any bookstore or library in Copenhagen (speaking of which, even if you're only going to be there a short time, you can apply for a card to lend books from Københavns Bibliotek. It's extremly
helpful). There's an English version, too, but honestly I prefer the German one, myself.
As far as pronunciation goes, you can likewise find a (sometimes multi-volume) Gyldendal Danish-only Ordbog (as well as others by other publishers) in any library in Copenhagen, which will
have the pronunciation of the Danish words listed. I wouldn't bother with buying one, though, as trusty old Ordnet
already lists the pronunciation for every word (frequently with audio recordings of the pronunciation), and is much easier to call up and search through at a moment's notice.