Have you tried pasting a text elsewhere (Windows editor)? Have you tried using hotkeys (<Ctrl>+<C> & <Ctrl>+<V>)? Or aren't you offered "paste" in the menu at all?
I just tried to copy/paste a word text and a text from a website and it worked.
sometimes I try to copy/paste smilies from another source than GTP and it doesn't always work. Sometimes it does.
I can copy but when I try to paste this smilie into the post, the paste thing isn't highlightened.
A couple of days ago I managed to copy a dancing banana and a woohoo in my post from another source. I can't find this post anymore but it worked without the image thing.
I think you may be able to paste an image if you are using the WYSIWYG editor. That would explain why it sometimes works and sometimes doesn't, because using the quick reply is not WYSIWYG, even if you have that set in your preferences.
And on a sitenote, the forum translates the appropriate text into smilies. You find the texts that represent the smilies in the smilie list. So it may be that you can copy smilies as they are recognised as a text, while a picture is just a picture (or a link if you will).