A Few years ago I helped a friend of mine move his yacht from Oman to Malaysia
.... which is effectively what you are going to do.
We left Early March - our route
was Muscat -> Cochin, then Cochin->Langkawi
in the Gulf to Cochin was lousy for sailing - we spent much more time without wind
than was comfortable. However with limited Diesel
we just had to wallow around.
After Cochin and rounding Sri Lanka, I believe the winds picked up.
Total Sailing time was 28 days !!! 32ft Yacht.
The Yachties in Malaysia/Thailand all used to (pre pirates) sail towards Salalah (southern Oman) and then to Aden after 1st Jan - So that would be the best time I believe for you to head
that was also.
Summer time would be horrible - due to the Monsoon in the gulf, India
and unpleasant unreliable weather
Hope this helps.