Cannot update iPad 1 to iOS 4.3 or higher
It won't be possible to updated to iOS 4.3 unless you have a software image for iOS 4.3 handy.  This is because Apple wants to force you to install the latest version which is iOS 5.0.  The test app you have been sent should still run on iOS 5.0 though.
Since iTunes isn't being nice about letting you upgrade, what you can do is go download the iOS 5.0 software image from Apple and then you can force iTunes to update using the image.  Here's what you do.

Download iOS 5.0 for your iPad from the following link (please be aware that this link is not a direct download from Apple.  Apple doesn't offer the ability to download iOS outside of iTunes which is why I've provided this link)
http://www.ijailbreak.com/ipad/download-ios-5-firmware/

Plug your iPad into iTunes.  Hold down the Option key on your keyboard and click the &quot;Check For Update&quot; button in iTunes.  An Open File dialog box will open.  Select the software image you downloaded in step #1.

iTunes should upgrade your iPad.