No option on App Store to update High Sierra to Mojave
Based on your post, your MacBook should be compatible with the Mojave update.


Once the App Store app finishes downloading and installing you should see a installer in the Launchpad (it should automatically open, otherwise try double clicking on it to manually start the installer).
 
If this doesn't work out you might want to look at making a bootable USB installer, and proceed with the installation after booting from the USB stick. See here (Apple Support Documentation)