Doctor heads first for part of the Midlands (13)

I believe the answer is:

staffordshire

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'part of the midlands' is the definition.
The definition suggests a singular noun which matches the answer.

'doctor heads first for' is the wordplay.
'doctor' is an anagram indicator.
'heads'+'first'+'for'='headsfirstfor'
'headsfirstfor' with letters rearranged gives 'STAFFORDSHIRE'.

Can you help me to learn more?

(Other definitions for staffordshire that I've seen before include "County E. of Shropshire" , "English county" .)

I've seen this clue in The Telegraph.

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