Here is how to jailbreak a 1.1.3 iPod Touch/ iPhone. Quoted from here.
“STATEMENT OF RISK
As all upgrades are risky, this one is doubly so. You may have to restore your phone using iTunes and start again if it fails. Make sure to back up first!”
Now the actual jailbreak:
“Here’s how you do it:
– Start with a 1.1.1 or 1.1.2 jailbroken phone with Installer.app installed AND AT LEAST 300mb OF FREE SPACE.
– Plug in your phone via USB to your computer.
– Download, extract, and run iBrickr Special 1.1.3 jailbreak edition (ibrickr.exe in the archive).
– iBrickr will determine what firmware you are running on your phone and make sure you can run the update.
– iBrickr will then guide you through the process of obtaining and modifying the 1.1.3 firmware (make sure to read everything thoroughly).
– iBrickr will upload the new firmware image to your phone. Note that this only puts the file on your phone and does not modify it at all, yet.
– When iBrickr finishes (should take about 10 minutes), it will tell you to go to Installer and install the “1.1.3 soft upgrade” package. Do that.
– The upgrade will stall at about halfway. THIS IS NORMAL. DO NOT INTERACT WITH YOUR PHONE WHILE THIS IS HAPPENING. Just leave it plugged in and leave it alone.
– When the installer finishes (this should take another 10-15 minutes), your phone should reboot with a fresh activated 1.1.3 firmware.”
There you go, a jailbroken 1.1.3 iPod Touch/ iPhone.