Is it a good idea to move high-volume and highly-accessed tables to a separate database?
You will gain a lot more with regards to performance if you move the table to a different harddisk. As long as the "busy" table and the rest are located on the same disk, moving that table into a different "file" (by moving it into a different database) won't change anything with regards to (I/O) performance. 

Distributing the I/O load to a different harddisk (and a different harddisk controller) will most probably give you a better performance for the remaining data because it is not affected by the I/O done on the busy table.

To move the table to a different harddisk, you need to create a new tablespace (which of course is located on that disk) and then move that table to that tablespace.