Complete iPad backup software without using iTunes, for Windows? I'm searching for Windows software to fully back up an iPad.

iTunes only saves those files which were transfered from the same Apple ID.

I need to backup songs, apps and photos. Perhaps the e-mail configuration, too.

I have to update an iPad from 4.3.3 to 5.1, without losing any data.
You can use iPad to Computer Transfer (ATTENTION: Direct download link). It's an easy tool which allow you to do exactly what you've asked for. Here is an excellent how-to guide.

And if you're looking for a more solid (and more expensive) solution, you can always try iPad Max.