You should schedule a couple of hour outage to do the installation. Yes, you can and should clone the vCenter server live in advance to speed up the process. Heartbeat gets installed on all VMs that you want protected.
The process I would take would be:
Spent at least two hours reading the documentation, verify all prerequisites are met; read the release notes.
These prerequisites include having IP information - at least 5 of them - 1 public IP, 2 Management IPs, and 2 channel IPs. (This would include at least 3 hostnames as well though technically, the public hostname isn't used, it needs to be added to DNS as a hostname.) If you're doing this with SQL, that would mean you would need the same information for the VMs as well.
Clone original vCenter server (V2V, P2V, P2P)
Install Heartbeat on primary server
Install Heartbeat on secondary server
Configure Heartbeat
Install Heartbeat on primary SQL Server
Install Heartbeat on secondary SQL Server
Configure Heartbeat
Install Client Tools, if remote management is needed
