The most common and most likely answer to this crossword clue is the 8 letter word TODDLING
I've seen this crossword clue in The Daily Telegraph
T
O
D
D
L
I
N
G
More clues leading to the result TODDLING
Buddy explains!

The straight part
We know that "walking unsteadily" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case walking unsteadily = toddling.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 TODDLING mean?
TODDLING verb- To walk unsteadily, as a small child does.
- To walk in a carefree manner.
- The unsteady walking of a child.