I don’t think there is similar functionality in Julia.
Also, for single line, you may not need the triple quotes (unless you want to use unescaped quotes), so
"stuff" f(x) = 1
would work fine, too.
Finally, if you still don’t like prepending docstrings, you can write a macro
@docafter f(x) = 1 "stuff"
but personally I would just stick with what’s supported.