Hey there,

Well. Try to think of it not as a career option. But to enjoy what you study. (since you are asking this question, we would presume that you still have not gone into Aerospace Engineering).
1) Aerospace engineering is one of the most satisfying engineering courses, as it was quoted by one of the Electrical engineers of IIT Madras.
2) It would make you learn the practical aspects of flights, designs, theory and architecture of the planes and ships, chemistry behind the fuels and many more, like every other engineering. But if you can relate to these things or passionate about it, then you should take a chance.
3) It may not have a very big job market (like IT or Consulting) but remember, after a few years in non-technical jobs, you can not come back to engineering jobs. Moreover, there are institutions like ISRO, HAL and IAF who hire Aerospace engineers. The vacancies could be less but you might have a better chance of doing what you love, rather than generic stuff and regretting it later.
Some of the institutes where this stream would be taught, are IITs, a couple of NITs, and I think, ISRO also has opened its own institute. Understand this fact; Becoming an engineer is not easy. You can probably get the degree but can not become a good engineer unless you work hard. It's a good enough career in India provided you get into some above average college and do not aspire to be a Pilot.It's a good career option in USA, Russia. Canada could be an ideal option if you are from India, UK is also a very good option, but it gives opportunity only to people from EU countries. Some of the leading universities which offer comprehensive masters programmes in Aeronautical Engineering in abroad  are:

Fulton School of Engineering, Arizona State University, USA

Clarkson University, USA

California Institute of Technology, USA

University of Glasgow, UK

Cranfield University, UK

Loughborough University, UK

University of Toronto, Canada

Choose wisely. All the best.

Thank you.