Crossword Genius

Name of one of those corgis Queen Elizabeth had? (5)

Ross

I believe the answer is:

peter

I'm a little stuck... Click here to teach me more about this clue!

'elizabeth had?' is the definition.
I can't tell whether this definition defines the answer.

'name of one of those corgis queen' is the wordplay.
I cannot quite see how this works, but
'name' could be 'pet' and 'pet' is present in the answer.
'queen' could be 'er' (short for Elizabeth Regina ie Queen Elizabeth) and 'er' is present in the answer.
No letters remain.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for peter that I've seen before include "Early Pope" , "Fellow < safe" , "Play high card before low" , "and 4 across Doctor Who actor" , "Safe; saint" .)

I've seen this clue in the Evening Standard.
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