The most common and most likely answer to this crossword clue is the 6 letter word FRUMPY
I've seen this crossword clue in The Guardian
F
R
U
M
P
Y
More clues leading to the result FRUMPY
Buddy explains!

The straight part
We know that "Dowdy" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dowdy = frumpy.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.
What does FRUMPY mean?
FRUMPY adjective- Dowdy, unkempt, or unfashionable.
- Bad-tempered.