Quicklaunch uses HTTP ports 80 and 443 for all its updates, licensing and error logging.
The one exception is the Network check. It can use ICMP or web request with HTTP port 80. This is configured in QuickLaunch settings.
Depending on the hardware being used (e.g. Biamp dialer, Tesira adapter) there may be a requirement for specific ports to be open. Consult the specific hardware manufacturers documentation for this information.
Depending on the software being used in Quicklaunch (e.g. Skype4B, Exchange, Google calendar, etc.) there may be a requirement for specific ports to be open. Consult the specific software manufacturers documentation for this information.