it wont hurt organising a doula sooner rather than later.
from when i started looking and when i actually found one i liked, it was probably about 2 months. i found it hard organising to meet with them as i was either working or they were working.

also, 'shop around' til you find someone you really like. it would be awful of you left it too late and had to settle with someone you werent 100% sure of.