Yes, solo trekking in the Gokyo valley region is doable. However, solo trekking in the Himalayas has its own sets of problems. First and foremost you have to do everything from the scratch yourself.  You have to fend yourself for your lodging, dining to trekking in the unknown and unfamiliar isolated paths. To avoid all these hassles it is advisable to join a group joining trekking in Gokyo Valley. Or else another best option is to hire a licensed guide or porter working for an authorized trekking company. Solo Trekking is undoubtedly thrilling and a raw experience but can be serious at times.