Do I need F1 Visa?

[Aash]

I was enrolled to start school, but due to family emergency I had to drop the school a few days before the start date. I have a valid F1 visa under the name of the university. I asked my DSO to defer me to the next term since I wouldn't be able to attend school and would have to leave for my home country. She is suggesting in that case I will be receiving new I20, new SEVIS ID and then would have to again get new F1 visa to reflect the new SEVIS ID. She also mentioned that she will be using SEVIS termination reason 'Transfer Student - No Show' and not 'Authorized Early Withdrawal'. 

I understand that I would require new I20 and new Sevis record for reentry. But, do I require new F1 visa as well? Also, can there be any issues for using Transfer Student - No show reason? What is the grace period to leave the country in this reason?
Timeline of the start dates: 
Initial Start date - October, and asked DSO to defer to January