I will have to strongly disagree with that. We did the transamerica (4,244 miles) last year at a pace a bit faster than that and it was not a death march. We all enjoyed it. I am was 56 and my companions were 21 and 22 so they were near your ages.
Granted we started out a bit slow in the beginning, but one of the riders was not even a cyclist 8 weeks before we left. She had a handful of rides in before the trip, but the longest was just a bit over 30 miles. She was in pretty good shape being a runner.
My other companion had ridden a bit more in her life, but not for a long time and had the same 8 weeks to get ready. She had been pretty sedentary that year (she is in great shape now).
They were both busy finishing their senior year of college and had very little time to train.
The bottom line is that they did great.
For a shorter trip like yours you will need to be able to start at a decent pace because the length of the trip will not allow as much training as you go, but your planned pace really isn't that bad of a pace. If you are used to riding all day it will be a reasonable pace.
All that said it is nice to have an open ended schedule. If possible allow 4 weeks, just in case, but expect to actually only use 3. You will be more relaxed and enjoy the trip more without a firm deadline.
BTW: My theory is that it is best to start out fairly easy and build as you go, riding at daily mileage that is manageable without days off. Days off break your rhythm and are counterproductive. If you need a rest take a 30-40 mile day, but only take full days off if there is something special that you want to do. Never take a day and veg out in camp or a motel unless it is forced by illness or injury.