Fastest way to becoming an astrologist?

[Risvertasashi]

Also, do I get any advantages as astrologist from levelling the WHM first or should I have started out as another role?

Fast queues, and AST's core healing spells are very parallel to WHM's, so the experience transfers.

Mostly, the best way to AST fast is to just play whatever will get you to Heavensward/Ishgard the fastest. Scholar would also do it, as would any tank.