Notes are contained in the iPad backup. They are not part to the transfer purchases feature which is exactly what it says it is for .... Transferring purchased content from an iDevice into your computer's iTunes library.
You can backup the original iPad with iTunes and then restore the new iPad from the backup of the old iPad. This will restore all device settings, app data, documents, notes, calendar entires, Safari history and bookmarks and everything that iTunes backup - onto the new iPad. After you restore from the backup, sync with iTunes and you should have two identical iPads - with the exception of passwords which will have to be manually entered on the new iPad. Passwords can only be restored to the device from which they were original entered and not to a new device.
Read this for more information
How to backup and restore from a backup
Also, if you are running iOS 5 on your iPad 1, and you have previously enabled iCloud Notes sync your iPad 1 notes should be in your iCloud account. Simply enable iCloud Notes sync on your iPad 3 to trasnfer the notes.
If you havent't previously enabled iCloud Notes sync on your old iPad, you can transfer your iPad notes to your new iPad without needing to restore from backup using third party applications such as copytrans contacts
Simply run the program on your computer, connect your iPad and export your notes in text files to your coputer.
After that use the same tool to import the notes to your new iPad.