I hesitate to recommend our solution as the site that created the software has disappeared off the face of the internet, it's completely unsupported, and I don't think it will have been tested on 2012.
Having said all that, I can send it to you if you wish.....
We've run it for about 5 years now, it was on our 2003 servers, and it's now running on 2008R2 with no issues.
There is a batch file that runs on the live DHCP server that backs up the DB to the standby server, you just schedule this for whatever interval suits you.
You install the service on the standby server, configure it with the live server IP, and the backup file location, SMTP server if you want alerts - and that's about it.
The standby server just checks every few minutes if the live server is up (With a bit of jiggery pokery for when the backup is running and DHCP is naturally stopped). If it's down it restores your backed up DB and starts up it's own DHCP service.
Once your Live server is back up, the standby DHCP service is shutdown again, waiting for it to be needed again.