Re: dan book?
Your simple question of what is a dan book opens a rather complex topic regarding organization affiliations, aikido styles etc.., as is witnessed by the other comments posted. If you are part of the World Aikikai organization and wish to be recognized for rank within that group the "dan book" is very important. It is a passport that indicates you are not only part of the aikikai, but it is something you will likely need to support documentation when you wish to apply for promotion. Most affiliated organizations have specific requirements as to hours of training and with who you need to attend seminar with. For example in my organization there is a specific requirement that we train during the 12 months prior to a dan promotion at least twice with the head instructor (Shihan) of our organization at seminar. The yudansha passport, when signed by the instructor, provides proof of attendance. While this may seem like just a detail of paperwork, it is a necessary item to have.
So if you have no interest in moving up in recognized rank with your new affiliated dojo, there is no need to worry about getting a passport. If you are, then you'll need to check into your new organization's policy regarding transferring a "non-affiliated" rank. If you are ranked shodan, most likely you will be asked to train for a while before being allowed to "test" for your dan rank; or, if they are generous "re-test" for the rank immediately.
The Aikido community is very welcoming and I have personally never had to show the passport in order to participate at seminars or workshops sponsored by other organizations. The one exception to this occurred at a special event that was open only to members of that specific organization. The passport didn't even come into play. I had to provide a membership card/number to participate.
In my opinion, rank recognition can become an ego thing. Our movement and demonstrated ability should be the standard that we use for evaluation. Yes it is nice to be recognized by others, but it is one's own opinion (and that of your primary instructor) that should matter.
Train with Joy!