Can I set up independent logs for my virtual hosted domains?

Yes, here's how:

The logging directives, TransferLog, LogFormat and CustomLog can be used inside virtual hosts just like you would use them for the primary domain. The way they interact with the logs set up outside the virtual hosts is like this:

If there are no TransferLog or CustomLog directives inside the virtual host, log requests for this host to the logs defined in the main server. Otherwise log requests to the log files defined in this virtual host and do not use any of the log files defined in the main server.

If Logformat is used in a virtual host, the format it defines is used for all TransferLog files defined inside that virtual host.

Otherwise the log format defined outside the virtual host is used by the TransferLogs defined inside the host, defaulting to the common log format if no LogFormat is defined in the main server.