I was able to do this just last night on a Level 1 twink I was testing (trying for the +1 stam Bracers). I had a Guild Lock summon my Level 1 out, locked his XP then Hearthed right back to Kezan and was able to do all Quests that any Level 1 can do there. Unfortunately at that point I got stuck because to continue on you have to be higher Level, the only Quest left in the first Starter Zone is Silver to my Level 1 and the second Starter Zone has an invisible wall blocking it. Sadly this means Level 1 Twinks cannot curerntly get the Best Bracers EverSadly, you cannot get back in to complete anything. Your hearthstone automatically gets retagged for (in my case) Stormwind.
I would suggest the same strategy for goblins: don't wear looms, and only do the exact quests and kill exactly what you need to.
A Level 1 cannot get to that part of the Starting Zone to continue the Quest Chain and get those Bracers. It's possible some Level 1 got them when Cata came out, before many of the current restrictions to the phased Starting Zones for Goblin, Worgen and Pandaren were implemented though.I checked wow head and it said quest is a lvl 1 quest so can a lvl 1 get it?