And you have the same iCloud account turned on on the iPad Mini that you have turned on on the computer with the iTunes library?
If the answer to this one is yes also, then log out of the iTunes store on the Mini
Make sure all other apps are closed - double click the Home key, and then press on the first app showing in the list. Click on the "-" (minus sign) on each of them to close them
Sign back on to the iTunes store on the Mini, and see if under Purchased/Not on this iPad, the items are now showing for download
If that does not work, then delete the iCloud account and re-add it to the Mini
Finally, if none of those steps work, then reset the Mini - press and hold down on both the Home and the Power buttons until the Silver Apple appears (you will not lose any data). Once the Home screen comes up again, go back into iTunes and see if you can now see your Purchased music.
If you cannot, then I would suggest hooking the Mini up to the computer with your iTunes library, and manually syncing the music to the Mini. Make sure that you have the "Sync Music" option turned on in the Music tab on the Mini's profile in iTunes on the computer (the one that shows when you hook the Mini up and then click on it), and that you have selected the specific music you want sync'd (all or selected)
One last thought - if your music library is on the Mac rather than on the PC, the issue may be because the Mac is running such an old version of iTunes.....
Keep me posted, and let me know if you have any other questions!
GB