Why am I not getting a Quick Start option on my iPad when I put my old iPad by it?

Is the old device running iOS 11 or later AND did you enable Bluetooth & Wifi on both devices?

Should be this case, and if you already tried (to no avail) ALL the steps provided in this support article:--> Use Quick Start to transfer data to a new iPhone, iPad, or iPod touch - Apple Support, contact Apple Support directly, using this link:--> Get Support

Regards

Giulio

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