It should be doable, but it depends on what speed you lose weight at as everyone is different!?
But taking into consideration this will be your first week and people report bigger losses on their first week, technically if you lost 4lbs in your first week then 2lbs thereafter, it would be doable in 6 weeks.
Personally id start today or tomorrow if I were you, that way you have 7 weeks... meaning an average loss of 2lbs per week!!!