Before I get into your questions, let me attempt to help in the defense against a Vulture rush. The general tactic I use in a Protoss versus Terran game is to get a Dragoon out as soon as possible. Send this Dragoon to the Terran base immediatly and have it hold position at the top of the ramp. Whilst doing this, have another Dragoon being created and range being upgraded. If you get 2 Dragoons on the top of a ramp holding position behind a Terran wall, the Terran is going to be a fool to make Vultures. He is going to have to start to produce Seige Tanks. This will most likely stop him from using a Vulture rush.
On to your question. If you want to rush Dark Templar(s), be sure to hide your technology buildings. By hiding I mean build them in a place where a scouting SCV or Vulture would most likely not go to. The top of your natural or the very side of your base is a good choice. Secondly, you should probably have 1 Zealot and 1 Dragoon, or 2 Dragoons at your ramp at all times in your tech stage so the Terran doesn't have a chance to see that you're not making many guys which would make him think you're teching.
So you've got your Templar Archives hidden and you make you're first Dark Templar. 1 Dark Templar on it's own is not going to do much, especially if you have to destroy a wall to get in. My adviec is to take the extra time to make a Shuttle and 2 Dark Templars. Load the 2 Dark Templars and a Dragoon into the Shuttle and drop them on the edge of a Terran base. Run your Dark Templar into the base and immediately go for Missle Turrets and ComSat Stations. If there are too many Missle Turrets, focus on killing as many SCVs as you can. Once the Terran mobilizes it's forces to try and counter the Dark Templar drop in its base, send the Dragoon and slow them down just a bit. This could mean the difference between killing all SCVs and half of the SCVs.
GL.