Can I use a backup of iOS 9 on a brand new iPad?

In fact my wife upgraded from an iPhone 4s with iOS 9 to a 6s with iOS 12, from an iCloud back up without any problem. It set up the 6s on iOS 12 perfectly, so I suspect you should be able to do the same. You certainly don't want to use iOS 9 on a new iPad.

You certainly don't want to use iOS 9 on a new iPad.

You can't install iOS 9 on an new iPad in any way, so that's not really a concern.

In fact outside of an iPad 2 or 3, or an iPad Mini 1 you cannot currently install iOS 9 on any other iPad.

As a general rule, Apple devices won't operate on any OS version older than what the device had loaded at the time it was shipped.

The other issue is that iOS 9 is largely 32-bit code and that won't run on newer iDevices designed for 64-bit code.

1. Restoring a backup only restores the data backed up, it does not in any way install the old iOS version the backup was taken on on the new device.
2. You can use the backup taken in iOS 9 on a device running iOS 12 without any issues and it will restore all the backed up data to the new iPad.
3. 32 bit apps will not work on iOS 12, and as such there data may not be accessible on the new iPad. Apps no longer available in the App Store will not be available on the new iPad.