I run CouchDB on my small production server, and I wish to periodically replicate it to my development server (running on another machine, inside my home). So what is the simplest method of doing it safely ?

I do not believe Replication can happen over HTTPS, a minimum of not. (In my opinion which include is originating with v1.1)

If you want so that it is secure (ie. encoded within the wire) you need to most likely use ssh/scp to periodically copy your database files for your development server.