Small pet (6)
(Other definitions for lapdog that I've seen before include "Small pampered pooch" , "devoted supporter" , "Submissive type" , "Infatuated person - small docile pet" , "One readily submitting" .)
'small pet' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for hamster that I've seen before include "Small pet rodent with pouched cheeks" , "Rodent often kept as pet" , "one running round in circles?" , "Common pet rodent" , "Little beast" .)