If you go to where Zevlor is standing here in the grove there is an exit to the left up some rocks. When you go out this exit Karlach's spawn point is a jump down the cliff on the right. You'll take like 90% damage if you don't have featherfall or something similar like misty step but you get to her super early and don't have to deal with any other combat.
I'll do anything to get to my favorite companion early.
Video link demonstrating the route to her:
Here you go. This is starting from Zevlor with a level 2 wizard with feather fall and enhance jump. Anyone else can get over there by jumping but you'll lose health and it's trickier to find the right spot to jump to.
https://streamable.com/ts7f5p
Edit: Anyone coming in later and wants to see the route just message me since the video link has expired.