Is it possible to transfer selected data from my iPhone 11 to my new iPad Air?

Natively available transfer methods are all-or-nothing. 

If you need to selectively move files, you must individually move/copy files using AirDrop, iCloud or iTunes (using a PC or Mac computer). Alternatively, transfer/restore everything, then selectively delete any data or Apps that you do not require. Consider also that many types of data and files can be synchronised via iCloud.

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

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