Sidecar can be enabled on older devices by modifying a default, as noted by Steve Troughton-Smith (@stroughtonsmith on Twitter):
defaults write http://com.apple.sidecar.display allowAllDevices -bool YES
Be aware that you'll probably need to restart your Mac for this change to take effect. Once enabled hover over the green zoom button for a window on your Mac, or click on the AirPlay icon in your menu bar. You should now see a list of destination devices.
Steve also listed the devices for which Sidecar isn't supported (at least in Beta 1). Check out his tweets for that if you're curious.
If you're not sure what your model identifer is, you can find that by running the following in Terminal:
ioreg -l | awk '/product-name/ { split($0, line, "\""); printf("%s\n", line[4]); }'
I was able to use these steps to get Sidecar running wirelessly between a MacBook Pro (13-inch, Late 2013, MacBookPro11,1) and a iPad Pro (12.9-inch, 2018), although it was very buggy. The iPad Pro didn't appear correctly in the list of destinations where a window could be sent. The quality of the video stream was very poor. It disconnected entirely several times. But Apple Pencil support did work for interacting with the macOS windows on the iPad. Overall it was useable, but a poor experience.
Even after changing the default the Sidecar preferences pane did not appear in System Prefrences, and it wasn't clear to me that there was an easy way to see it. But if you really want to try out the feature the steps above should work.