The pictured headset is for a 44mm headtube, you need one for a 34mm headtube. I would consider the stock headset to be a product that is designed to fail, 1/8" bearings are too small to hold up in a headset.

You want an EC34 headset intended for a 1 1/8" threadless fork. For something really solid and inexpensive, FSA Hammer is a good choice. Or for something a little more fancy with cartridge bearings, Cane Creek 40 is solid. There are plenty of other headsets out there that will work too.

The tools needed to replace a headset can be quite expensive, it would be worth considering taking the bike to a shop for the labor, even if you normally work on your own bike.