What I meant was links between your multiple backups. The explicit example you just gave is only one backup.
However, looking into it a bit more, it's pretty clear this isn't the issue. You are simply creating new directories and doing new full backups.
Check out the link mathewg42 gave to Mike Rubel's web page. Or get a copy of the O'Reilly book "Backup & Recovery" by W. Curtis Preston. This is all spelled out in Chapter 7 which covers rsync with snapshots, rsnapshot, rdiff, etc. rsnapshot implements the whole procedure and may be available with your distribution.
If you want to script it yourself with rsync, the basic idea is to first create a full backup with rsync. Then replicate the full backup using only hardlinks. Then rsync to the replicate letting it delete the links for those files that have changed and copy the new files in. Repeat the process on the most recent replicate of the backup. I would also change the -rv that you are using to -av. That catches more options that you want for a backup.
so, initially
Code:
BACKUPDIR=~/test/backups/`date +%R:%S`
rsync -av testsrc/. $BACKUPDIR
then
Code:
NEWDIR=~/test/backups/`date +%R:%S` {this will be different now}
cp -al $BACKUPDIR/. $NEWDIR/ {copy is all just links}
rsync --delete -av testsrc/. $NEWDIR {replace links only for changed content}
There are variations on this, and there are options in rsync that will create the links. And there is also rsnapshot. And, of course, jumping off in other directions, BackupPC, Amanda, . . . which can get more complicated.