It really does depend. A few airlines(Indigo, AI Express etc) are hiring type rated CPL-holders. However, if you're waiting for non-typed jobs to open up, it may take anywhere between 1-1.5 years.
IIRC, to add that (H) to your CPL, you need 50 PIC hours on helicopters in addition to the normal exp requirements. The issue is whether an operator would be willing to take you on with only those many hours. Frankly, I'm not really sure about that. I'll wait for someone who knows a little more to comment.