New H1B transfer before/after 1st Oct 2013 (current H4 visa)

[anjpat]

Hi,

I am currently on H4 visa and have got H1B approved through a consultancy valid from 1st Oct 2013.

Now, I am getting a full time opportunity with a big organization who are ready to transfer my H1B.

Please can you tell me -

1. Is it okay to transfer my H1B directly with the new employer without working for the current one?

2. When should I apply for transfer before 1st Oct or after ?

Many Thanks!