Is it possible to finish the Domain of Anguish quests with heroes

They are indeed mutually exclusive; everything you stick in your hall will only count once, including mini pets. You'll need 50 distinct ones to get all the points for it, as well as distinct armor sets for the armor monument and all heroes and special pets displayed in that particular monument as well.

Like most things in Guild Wars, it depends on whether that hour a day you can spend can be extended at all. The fastest current way found is to repeatedly farm the first few enemies on the Farmer Hamnet quest, detailed here - claimed LDoA in 2-3 days:

http://www.guildwarsguru.com/forum/fastest-way-ldoa-t10473064.html?t=10473064&highlight=ldoa+speed

Other than that, if we discount the exp you'll gain from killing foes for the sake of simplicity, you'll need 101,000 experience to get from level 10 to level 20, and at 1,000 experience per day, you're looking at about 101 days, probably quite a few less since you'll be killing some monsters to gain exp along the way. Cut that number down further if you have some time to go Charr hunting in the Northlands; it's a great way to get up to 14 or so in a few days without being as boring as farming one mob over and over again. At an hour a day, plan on devoting 2-3 months at it, and you'll probably be pleasantly surprised.

Almost forgot to mention, class matters a bit more in pre as well. If you're, say, a Ranger, you might be able to take advantage of the bonus weapons that come with pre-ordering some of the games if you did that, or owning collector's editions. AoE scatter also doesn't exist in pre, so quite a few people like running Elementalists or Ele secondaries for that reason.