not really. Everytime you update the firmware, it wipes out the installer.
Since you are on 1.1.1, this is what I recommend:
1) write down everything that shows in the uninstall section of installer and under Sources
2) Locate and install the OkToPrep app. This will prepare you for jailbreaking 1.1.2
3) download the 1.1.2 jailbreak.zip package and unzip it to a readily available folder. if you are on Windows, make sure that you can see the Windows.bat file in there.
4) Download the 1.1.2 ipsw file and make sure it's readily available.
5)connect to iTunes and sync.
6) since you have installed OkToPrep, you are ready to update.
7) hold down your shift key (generally the left one) and then click on update(or restore -either might be displayed) and a window will open up to browse to the ipsw file you want to use. Locate the 1.1.2 ipsw and select it and then click ok.
8) Once the update has finished and it's restored your profile back on the iPhone, close iTunes and keep the phone connected.
9) locate and double-click the windows.bat file that came in the 1.1.2 jailbreak.zip file that you unziped. This will jailbreak your phone in 1.1.2. Follow any prompts it gives you, and then, once it has finished, re-install your sources and programs that you installed in 1.1.1
10) you are done.
oh ok you scared me for a second there. I upgraded from 1.0.2 to 1.1.3 Jailbroken in about ten minutes. I know it was risky but I took the chance because my friend said he would sell me his for $100 if I bricked mine. but it worked out fine and I have had zero Problems. glad that you finally got to jailbreak again too. Happy Apping.