Special feeling or not shouldn't even matter, I have started to gear a level 5 priest and I'm enjoying it so far.
Next sunday I will be going for the LFH for the first time on that toon, I have the rare drops and am honored with the Timbermaw Hold.
Seeing progress on a twink is fun at, I think, any level. I'd advise anyone to try both a level 1 and a level 5, and if you want to try a priest, level 3 might be interesting too. You could start at level 1, and if you feel the urge to level for whatever reason, do it.
If you like being level 5, you are happy with your twink, if you regret having leveled up, reroll, after all it doesn't take that long to get some starters gear.
Use gear that doesn't bind if you think you might have trouble getting some enchants again.
And if you get in a little fight, and your mom gets scared, I'd advise you to go to your auntie and uncle in Bel Air.
That's pretty much it.