ORIGINAL REPLY:
There are two things you can do here - one is to copy the file db/uuid from the old server to the new one if you're just transferring the svn repository to a new machine and you plan to turn off the old one. The other thing depends on the SVN version you're using. If you're using 1.7 then use svn relocate (see docs), or for older clients use the --relocate option of the svn switch command which is intended for this scenario.
EDIT:
I misunderstood -- you want to recreate your repository with the trunk/branches/tags structure. In that case, dumping and reloading the project won't help as it won't magically create the new structure -- it'll just recreate what you already have. You can though easily create the new structure either in the repository browser (if you're using TortoiseSVN) or directly from your working copy. If you're doing it from the command line the syntax will be something like this, depending on the exact directory structure. Replace http:.../ with the address of your svn server. Oh, and back up the repository first!
# check out top-level directory
svn co http://.../
# make new trunk dir and move all contents to it -- note spelling of 'trunk'
mkdir trunk
svn add trunk
svn mv * trunk
# now create tags and branches
mkdir tags
mkdir branches
svn add trunk tags branches
svn commit -m "Created new repository layout"
Now all you should need to do to switch existing working copies over is:
svn switch http://.../project http://.../trunk/project
