Welcome, Baxi!
You have one of THE best vehicles around. Alas, it is not available any more!
Go right ahead, and stop worrying.
Just have your car checked up and serviced before you start.
You'll see many Qualises on the Manali-Leh route, and if you ask any taxi driver there, they'll tell you that the Qualis was the best!

There are many plying at Leh also.