Hi Sid:
Welcome to the forum community.
I don't think you should have any worries about your planned trip - you appear to have thought it out carefully, you'll not be too far from home (it's not like you are going to China or Ukraine or Zimbabwe on your first tour), and you have lots of time - your travel plans are not overly ambitious.
Personally, I think a fractionally larger motorcycle, perhaps 250cc, might be a better choice. 125s are generally considered to be "city bikes" and I think you might feel a bit uncomfortable on highways, where the 125 would be wrung right out trying to keep up with 60 MPH traffic. That is my biggest concern - having done a cross-Canada trip on a Honda 360 cc bike many years ago when I was much younger, I still clearly recall riding along at wide open throttle, with no reserve left, trying to keep up with the 70 MPH traffic. It was not a reassuring ride.
Don't forget that you will be carrying some luggage, and chances are the total weight of all your luggage, riding gear, etc. will come in somewhere around 50 pounds. That extra 50 pounds will have a significant effect on the acceleration & sustainable cruising speed of a 125cc bike.
There's not much weight or size difference between a 125 and a 250, so you don't need to worry about a 250 being more "difficult to handle". There's not much of a price difference either.
What is important to you is that you ensure that the motorcycle is fully inspected and serviced before you set out. This means having tires on it that will take you through your full trip, getting any and all "little gremlins" fixed, and having the engine, drive train (chain) and suspension fully serviced before you go. This is not a big concern if you buy a new bike, but it is critical if you buy a used bike.
Michael
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