I’d missed this somehow: there’s now a setting in 1Password’s Android app under Filling labelled “Auto-copy one-time passwords” that does exactly that (just as the Mac version has done for a long time):
If you’re using two-factor authentication (and you should be: if you’re not, look it up and figure it out, or ask someone to explain it to you), using 1Password to generate your one-time passwords is light years ahead of using a standalone app like Google Authenticator, and this feature makes it double amazing.