Gee! Douglas' cat is bad-tempered (6)
I believe the answer is:
grumpy
'bad-tempered' is the definition.
('grumpy' can be a synonym of 'bad-tempered')
'gee douglas' cat' is the wordplay.
'gee' becomes 'g' ('g' can be a synonym of 'gee').
'douglas' cat' becomes 'rumpy' (nickname for manx cat).
'g'+'rumpy'='GRUMPY'
'is' is the link.
(Other definitions for grumpy that I've seen before include "Bad-tempered, sulky" , "Ill-tempered and crabby" , "likely to snap?" , "Doc's irritable pal" , "In a bad mood" .)