The simple answer is AFAIK no, or not easily. Please correct me if I am wrong.
You are going to hit two problems: moving the dates, and isolating the users.
Bearing in mind the fact that Moodle is designed upon a social constructionist pedagogy, where users are encouraged to learn through social interaction, isolating users from one another is not going to be a Moodle forte'.
It is possible however to divide courses into groups, and even to create a group for each student. This will mean that each student will only see only the work of the other (non existant) students in their group. In Moodle 1.6, or using a hack it is or will be also possible to prevent students from seeing some of the activities in other groups.
It is much more difficult to change the times of the activities between groups. At the moment activities shared between groups are the same. The only way I know of at the moment is Bernard's super calendar, which really is super. By using an extension of the calendar block and some hacking of the course, it gives full but ASAIK manual control of the dates of activities within groups.
Alternatively shoudl you wish to pursue the possibility of making seperate courses, one for each student, then this can be achieved quite simply if a little labouriously by using backup and restore. You can then change the times of the activities in the groups by using Audun Hauge's or Brian Koontz's helpful hacks to make date changing easier. You might also consider using SQL commands to change dates globally according to conditions (see my tips nad tricks). Recently the cheif of the Web Based Training committee at my institution has recommended a piece of software costing about $50 that enables one to connect MS Excel to the database and make changes via that route.
If you search for WP1 (which is in fact a kind contributor's name) then you will find helpful summaries of methods and hacks for easing the process of course management.
But perhaps, returning to my initial point about the social constructionist pedagogy, one might say that Moodle was not designed for the factory farmer, but to make free-range more freer and at the same time more manageable.
BTW blease may I recommend that, if you have time, you do a bit of a search on the forums prior to askign a question? Your recent questions are ones that get asked a fair bit.