I am looking to travel to Dalaran without a mage port from Orgrimmar as that is where my hearth stone is set. What is the fastest way to get there?
If we asume you got no other transportation device then your flying mount, you'd simply jump on the "shark" Zeppelin to Borean Thundra and fly from there.
If you visit Dalaran rather often, I strongly suggest you to place your Hearthstone there, since there's a portal to Orgrimmar in Dalaran.
Other ways of getting to Dalaran; the engineering Worm Hole which allows you to chose one of a couple of randomly given zones of Northrend, which is rather close to Dalaran itself. Avoid choosing Howling Fjord and Borean Thundra since they're the most distant ones from Dalaran.
If you've grinded like a madmen with Argent Tournaments in Ice Crown, you can use their tabard to teleport there.
There's no point mentioning warlock summoning, but there's also the guild ability Have Group, Will Travel which allows someone positioned in Dalaran to summon you.
If you got silly much money and for some reason don't like to pay mages a small sum, you can on your next visit to Dalaran purchase an expensive ring which allows you to teleport to Dalaran.
I asume that you're a high level since you ask for the fastest way, and not the safiest way.