Change jobs before interview

[newbie2005]

Hello folks,

I need some advice and I hope someone can help me.

Here is my situation -
came to US on F1 and completed school
Oct 2004 - got H1 in
Sept 2005 - scheduled appoinment for visa stamping in Mumbai
Dec 2005 - visa stamping appointment date

Now, last week, I got an offer from a very good company and they want me to start in Dec 1st week.

My worry is that when I scheduled my interview at Consulate I sent the required docs - I797 from my current employer.

Question - can I change jobs before the interview and take new I-797 (assuming that my H1 can be transferred in 20 days)
Also, I will not have any pay stubs from new employer so would that be problem.

Please let me know what you guys think I can/should do?

Thanks much for your time.