See Help:Importing and exporting pages, it should help!

But it sure needs a lot of downloading and uploading, it is basically downloading the content of the page then uploading it to another wiki

I did that, instead of downloading I just opened the file through my web browser, copied it, pasted it in source, converted to visual, deleted some background code and voila, it works.

That would work more fantastically than download-upload technique

It does. Also, importing is reserved for only admins.

To answer the original question, I believe there is no standard way to move a page to another wiki. Techincally it should be possible to automate that with JavaScript, if someone will want to write one, but I doubt there are enough people who need it.

Nah its fine I understand now.

When you copy-paste using the editor, the new location simply shows one edit by you. When you export/import a page, the attribution of the edit to the user who actually made it is retained. If you export the full page history, the entire history and previous versions of the pages are also retained.

In the scenario mentioned, you would need admin at the destination wiki only... I think you can export without being an admin.

You can.