Tim,
Hair grows at approx half an inch a month, so I would say that a couple of months would be sufficient time to grow back your existing hair to a reasonable length and hide any evidence of your transplant. You're in the fortunate position of being able to stay off work for that amount of time so I'd say you'll be fine. You may even have some early growth from your transplant to complement your existing hair.
All the best whatever you decide.
Pete