Zoology

B.Sc. Zoology is more inclining towards modern technology, so after doing zoology you can choose any specialisation course in genetics, biotechnology, Endocrinology, Immunology, applied zoology, wildlife Science, Ecology and you will be eligible for all these specialised courses in most university.

You have not write about the college/university name from where you wish to pursue the M.Sc. Genetics course. However, the eligibility criteria of DU's is given below for reference please.
Eligibility criteria of M.Sc. Genetics: A student seeking admission of M.Sc. (Genetics) must have passed B.Sc.

The following Universities offering M.Sc. Courses without entrance exam.
1. University of Delhi
2. SRM University
3. Manipal University
4. Vellore Institute of Technology.

Yes, you can pursue your M.Sc from LPU after completing B.Sc in CZG. All the specializations have its own importance and scope. Rest it depends on your interest.