Hello Aimaan,
MSc. Bioinformatics has more scope,this is a rising industry in India and as of now a bioinformatics student has a great chance for further studies and working also in the foreign countries like Germany,United Kingdom,etc.
Zoology is about animals,their classifications,habbits and other details.
Bioinformatics is more about the biology and Information Technology,there are databases,auto-docking other softwares for drug designing etc and so Ph.D in Zoology after MSc. Bioinformatics is not at all a good idea.
Bioscience covers biochemistry,bioinformatics,genetics,immunology,zoology,cell biology and so if in your bachelor's degree you have studied zoology in a large extent then Ph.D in zoology after bioscience can be done.