Hindu covering Indian bread right away (5)

I believe the answer is:

dhoti

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'hindu covering' is the definition.
'dhoti' can be an answer for 'covering' (dhoti is a kind of covering). I'm unsure of the 'hindu' bit.

'indian bread right away' is the wordplay.
'indian' becomes 'dh' (I can't justify this - if you can you should believe this answer much more).
'bread' becomes 'roti' (roti is a type of bread).
'right' becomes 'R' (common abbreviation).
'away' is a deletion indicator.
'roti' with 'r' taken out is 'oti'.
'dh'+'oti'='DHOTI'

Can you help me to learn more?

(Other definitions for dhoti that I've seen before include "Lean over; end of loaf" , "Cloth round middle" , "Skimpy item of clothing" , "Hindu loincloth" , "Indian loincloth" .)

I've seen this clue in the Sydney Morning Herald.

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