Dog's cross: that is, a little labradoodle (7)
I believe the answer is:
spaniel
'dog's' is the definition.
(spaniel is a kind of dog)
'cross that is a little labradoodle' is the wordplay.
'cross' becomes 'span' (span can mean to cross or bridge).
'that is' becomes 'ie' (abbreviation for id est, 'that is' in Latin).
'a little' says to take the initial letters.
The initial letter of 'labradoodle' is 'l'.
'span'+'ie'+'l'='SPANIEL'
(Other definitions for spaniel that I've seen before include "See 13" , "Droopy-ear dog" , "Dog with drooping ears" , "Dog with long silky coat" , "Animal" .)