When you click "browse steam workshop" one of several things will happen:

1) It will open in steam overlay (if overlay is currently working)

If overlay is not working:

2) It will open workshop in the steam client browser itself. So check that.

(It should use your default web browser to launch the steam client, via a steam url. )

First, Thanks for your kind. Now I know what thing will happened. It just make me feels clear anyway.

My situation was that I logged-on steam client browser, goes on my library, run DQ, and meet the problem.

"1) It will open in steam overlay (if overlay is currently working)
If overlay is not working:"

yes. i checked overlay option in steam setting. but overlay didn't appear.

"2) It will open workshop in the steam client browser itself. So check that.
(It should use your default web browser to launch the steam client, via a steam url. )"

so i expect steam client browser goes to workshop page. but it didn't, too.
futhermore, any of my web browser - IE, Chrome - were same. nothing happened.
I re-Installed steam client browser and DQ, retry it. but.... sadly. result was same.

personally, i guess this problem's reason is my too old pc. '1gb ram' is too small for steam client browser. - frankly, DQ is also heavy for my pc. But i love this game haha.
Anyway, Thanks for - regardless of my bad English - answer. I should buy new pc. DQ has worth for it. I believe new-fast-pc will solve this problem.
Thanks for reading.

Hey, no problem!

What I can do is try to make a button that just opens workshop in your regular internet browser, and release that in the next patch.