Hi Shweta,
Being from a premier institute is an advantage, but not the sole criterion for achieving one's dreams. Most corporates look for relevant experience and talent, which is not institute-specific. With the right skills and attitude, there is no stopping you, lady :)
If we hone our skills, HR and interpersonal, keep ourselves updated about the industry news, and maintain a learning attitude, we can achieve a lot. The 1-2 years that you'll spend in your current company, try to learn as much as possible. One advantage that you'll have is that you can experiment with ideas - you'll have a lesser number of employees to administer them to. Also, small companies and startups require HR functions to be developed and implemented from scratch, which gives awesome hands-on experience. So all the best. :)