You can do it early... even untwinked. The broom or stein or whichever focus item you are after mainly costs 200ish pp for the central item of the quest. If you go and farm up a bunch of bone chips (they sell 4-5pp each) you could do it. Or go around grabbing things and reselling (like there is a stein that drops from guards in the feerrott that has a lot of charisma
https://wiki.project1999.com/A_Crude_Stein , they rot almost always since they are lore and drop every time).
Or go sell peoples scythes for them in feerrott or offer to exchange silver / gold / platinum from people doing long camps....or bringing people stacks of food in far off places. All this stuff you can do at level 5 (since you need that level to enter some dungeons). Sure you might die, but in the end you will raise the platinum you need.
I'd also hang around cazic thule if I were you, maybe even find someone with an extra they don't need that is rotting (this happens if someone is powerleveling an alt at the gators, the items are lore so they sometimes rot...boom, that's your big cost item out of the way).
The other things are smaller and easier to get (giant toes or things like that you can get by going to the zone and seeing if anyone has an extra....just explain you are on a quest!).
Even showing up to zones and asking nearby people if they could lend a hand slaying something or another usually works. You might have to sit around a while until someone not busy passes nearby, but eventually you can find someone.
I do lots of low level questing. The adventure!! The excitement!!!