May I delete the Dorico 1.x app after 2 (Pro) is installed?

I have two applications, running macOS High Sierra, one for Dorico 1.x and one for Dorico 2. May I delete the old and not run into any problems?

Yes. Just drag it into the trash.

I’d keep it around for a while “just in case”. That is, unless the trash bin has already clanked shut.