Well you're lucky, a law was just passed a few months ago that actually allows women to ride bikes here in Qatar, before they weren't allowed without special permission.

Not sure about the issues with importing...if they are the same as the cars the bike must be either less then 10 or more then 30 years old. I suggest you google the Harley store here and ask them, they should know everything.

As for your wife attracting attention, she will no matter what, however as long as she dresses conservatively she can't be arrested. But my guess is she'll be harassed by every douchebag with a land cruiser is Qatar.