Trello – Create Template Board and Cards on Trello

Moving a list to another board is not currently possible, but it's an idea that's under consideration

Zapier can sort of do this with https://zapier.com/z/60m/zapbook/schedule/trello/9149/create-trello-card-every-month/, while you won't be able "copy a card" on a schedule, you will be able to customize it in the Zapier interface.

You can of course modify the card however you like, inserting special variables like current month, day of week or time, but you can also add lots of other options like labels and such.

Disclaimer: I'm a co-founder of Zapier but use Trello a lot personally (it rocks!).