Yes, Quark does have an easy as pie way to turn off Hyphenation. Under the Edit menu, select H&Js (hyphenation and justifications) then double click on No Hyphenation. This will open a window that shows the current settings for No Hyphenation. If the Auto Hyphenation box is already Unchecked, just click OK or press Enter. If there's a check in the AH box, just uncheck and click OK.
Now click the Save button and you're all set. Easy peasy. This is just one of the many many reasons I prefer Quark over ID. But that's me.