The most common and most likely answer to this crossword clue is the 8 letter word SEALYHAM
I've seen this crossword clue in The Daily Telegraph
S
E
A
L
Y
H
A
M
Buddy explains!
The straight part
We know that "little dog" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case little dog = sealyham.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.