Soloing is tough at 19, even with pretty good gear. You can start doing the quests in your mid 20s, or earlier if you hang out in the heavily-trafficked zones and ask in /ooc to loot the pieces you need. A number of the camps will be really tough to solo until the mobs are green.
Honestly though, unless you really want to do the quests I'd recommend against them. They take quite a bit of time (I did nearly all of them) and the gear won't make a significant impact in your soloing ability at this level. From an efficiency standpoint, you're better off getting a few more levels, saving more money, and buying the inexpensive Jaundiced Bone pieces for the AC (Boots, Gauntlets, Vambraces, and maybe the Helm).
Since you're Barbarian, I'd suggest you go to Karnor's Castle and loot the
Jarsath armor that frequently rots. The bracer and leggings in particular will last you a long time, and you can't beat free.