Any dungeon that is apart of the Main Story Quest line will have duty support. Any of the optional dungeons will not. The Hard trials and the Crystal Tower raids also isn't. Though don't take that as a sign for any manner of difficulty. As most are easy enough to it shouldn't matter how often you die. Most players probably won't even get mad or gripe about the deaths either. The game currently has the dungeons that unlock from following the main story up to the lv 57 dungeon in the Heavensward expansion flagged for duty support. The next batch to get this treatment will come with the 6.3 patch. Always remember to let people know your new to a fight as it helps set expectations. And try to be open to any advice given if someone feels you could be doing better. I do know there is at least one solo trial down the line.