Welcome to the wonderful world of the Model T. Two door? If it's an American T, it has either one door (roadster, also called runabout) or three doors (touring) because there's no driver's door. If it's Canadian, it will have a driver's door. Convertible is a modern term.
The answer to your question is yes, it should fit with the windshield up. My 1915 roadster is 6'2", so I expect the 1919 will be about the same.
I always tell new T owners that the first Model T parts they should buy are these. The Ford manual and the MTFCA books will save you a lot of grief hassle, and expense. The T is pretty simple, but different. If you just dive in and start working on something without any instructions you can do some unintended and easily avoided damage.
I expect you will have lots of fun with this car. If you have any questions the books don't cover, you can usually find the answer here and on the other T forums.