Can i restore a new ipad from an old ipad?

These support pages should get you started with setup of your new iPad - and the methods of transferring your data from old to new iPad:

Set up your iPhone, iPad or iPod touch – Apple Support

Transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch - Apple Support

Use Quick Start to transfer data to a new iPhone, iPad or iPod touch – Apple Support

If the donor iPad, from which you are transferring your data precedes iOS12.4, QuickStart will not be available.

“Transfer” is rather a misnomer. In reality, your data and setup is merely cloned to the new device. Nothing is moved or removed from the original device.

An alternative is to restore either an iCloud or iTunes backup to the new device:

How to back up your iPhone, iPad and iPod touch – Apple Support

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

SteveShapiro wrote:

The instructions seem to say that the new iPad must be upgraded to be the same as the old one. Can an iPad be "downgraded"?

No. A new one will most likely be loaded with iPadOS 15 and there is no means to roll it to an older version.

Yes. An existing iCloud or iTunes backup, created from your old iPad, can be directly restored to your new iPad.

The response that I have already provided does not suggest that your old iPad needs to be updated - but outlines all the methods that are available to you in transferring data (or restoring a backup) to a new device.

Be aware that initial setup of a new iPad will usually prompt update to the most recent version of iPadOS prior to transferring/restoring data from a backup.

SteveShapiro wrote:

Ok. so my backup of my old iPad is worthless? It's a complete backup, not a partial cloud backup.

It could be used to transfer data. Photos, videos, and notes, as well as generic saved files are the most compatible. App data usually transfers fine with new app versions, but there could be little incompatibility issues with newer app versions, such as data that is no longer used and discarded.

I’ve had some really old apps where it even reloaded the apps on a restore to a newer OS, but the app didn’t work. They’ll usually transfer over properly to a newer version of the app. I even have a few that are no longer available on the App Store for new downloads, but reloaded just fine from the App Store after a restore from a backup, and where the app fully works.

Quite correct - and neither does it need to be updated for any of the available transfer methods (including a backup/restore) to be used.

The only transfer method that may not be available to older iPad models is QuickStart - and this too will be available if your iPad has been updated to iOS 12.5.5 (this being the final update available for your iPad Air1).