How do I add timestamps to individual lines of PowerShell & output?

You could use a filter:

filter timestamp {"$(Get-Date -Format o): $_"}
$result = & ping 192.168.1.1 | timestamp

Sample output from $result:

2014-12-08T11:42:59.2827202-05:00: 
2014-12-08T11:42:59.2857205-05:00: Pinging 192.168.1.1 with 32 bytes of data:
2014-12-08T11:43:03.1241043-05:00: Request timed out.
2014-12-08T11:43:08.1236042-05:00: Request timed out.
2014-12-08T11:43:13.1241042-05:00: Request timed out.
2014-12-08T11:43:18.1246042-05:00: Request timed out.
2014-12-08T11:43:18.1246042-05:00: 
2014-12-08T11:43:18.1246042-05:00: Ping statistics for 192.168.1.1:
2014-12-08T11:43:18.1246042-05:00:     Packets: Sent = 4, Received = 0, Lost = 4 (100% loss),