Head: Lucky Fishing Hat, reward from Rare Fish - Keefer's Angelfish quest, with +8 agi Lesser Arcanum of Voracity, obtained from quest Libram of Voracity.
Neck: Sentinel's Medallion, obtained from PvP. Costs 65 Honor Points and 20 Warsong Gulch Mark of Honor.
Shoulders: Serpent's Shoulders, obtained from Lady Anacondra in Wailing Caverns located in The Barrens.
Back: Sentry Cloak (rare drop, be lucky, or buy from AH), +12 Dogde Rating enchant.
Chest: Tunic of Westfall, Alliance only, though (The Defias Brotherhood quest). If you're horde, go for Blackened Defias Armor, drops from Edwin VanCleef in The Deadmines. Either +4 all stats enchant, or +100 hp.
Wrist: Forest Leather Bracers, random drop from monsters/lockboxes/chests, be lucky or buy from AH. +9 stam enchant.
Gloves: Gloves of the Fang, drops from Druid of the Fang in Wailing Caverns. +15 agi enchant.
Belt: Deviate Scale Belt, made from leatherworking. Do it yourself, get someone to do it or buy from AH.
Legs: Scouting Trousers of Agility, random greenie, be lucky or buy it from AH, if it's there. An alternative is Dark Leather Pants. The only difference is that the Scouting Trousers of Agility got 1 more armor, than Dark Leather Pants. Nethercleft Leg Armor (40 stam, 12 agi) enchant.
Feet: Nat Pagle's Extreme Anglin' Boots, reward from Rare Fish - Brownell's Blue Striped Racer quest. Cat's Swiftness enchant (+6 agi, minor run speed).
Rings: 2xMeadow Ring of Eluding, another random greenie, be very lucky for them to drop, or buy from AH, if you're lucky there's any there.
Trinkets: Insignia of the Alliance, PvP reward, costs 2,805 Honor Points, and Arena Grand Master, obtained from the Arena Grandmaster quest, where you need to get 12 Arena Masters, which it is possible to get 1 every three hours, from a chest in the Stranglethorn Arena. It goes like this. One chest spawn at 3 AM, then 6 AM, 9 AM, 12 PM, 3 PM, 6 PM, and 9 PM (server time). Usually there's a bunch of 70's around there, just for messing it up for the twinks going there for the Arena Masters.
Weapons:
Main Hand: Shadowfang, is a random blue drop from Shadowfang Keep located in Silverpine Forest just southeast from Undercity. Together with the +15 agi enchant, this weapon makes the best lvl 19 rogue twink main hand.
Off Hand: Thief's Blade is a drop from Mr. Smite in The Deadmines. Put +15 agi on this precious little blade, and it makes the perfect off hand for lvl 19 rogue twinks.