iTunes is not Updating on a Window's Vista Laptop; Says I need Windows 7
You should be fine:

Windows System Requirements
PC with a 1GHz Intel or AMD processor and 512MB of RAM
Windows XP Service Pack 3 or later, 32-bit editions of Windows Vista, Windows 7, or Windows 8
64-bit editions of Windows Vista, Windows 7, or Windows 8 require the iTunes64-bit installer
400MB of available disk space
Broadband Internet connection to use the iTunes Store 


http://www.apple.com/itunes/download/

Just figure out if you need the 32 bit version or the 64 bit version. The download website should detect for your system though.

Also make sure your laptop and your phone are Authorized on your Apple ID.

UPDATE Related to OP's comment:

Don't try to upgrade from inside iTunes itself. 

Exit out of iTunes, even better restart your laptop. 

Go to the website, download the installer

Use the installer you download to update.