Import export one click backup ?

It's been added to GPP 1.6 :)

Tom, will this premium module/one click backup work equally well if one is using a child theme?

Yes, child theme shouldn't matter.

1.6 beta is available for testing if you'd like to check it out: https://generatepress.com/gp-premium-1-6/

Thanks.
When do you expect 1.6 to come out of Beta?

Within the next couple of weeks :)