1and1 are a nightmare to deal with in terms of transfers.....the customer service is shocking and they have "lost" a couple of my domains in the past while I was trying to transfer them internally to a new account I had created for business use to seperate them from my personal stuff. One of the domains was/is of no real interest to anyone else but for over 3 years now it has been unavailable for me to re-register and a whois search turns up "registered but no website" but gives an error of "Domain or IP Address not found"
I never purchase a domain either through 1and1 or from someone who has it registered currently at 1and1 due to that and the many horror stories you can read about similar cases around the web.
The best I can suggest is that you follow their instructions to the letter, that way, should anything go wrong then you at least have some comeback in that you did what they requested instead of looking for a "wuick and easy" method which backfires.
Good Luck