How to initiate node_save() on module install?
If it's your own module, use hook_install():

Perform setup tasks when the module is installed.

or hook_enable():

Perform necessary actions after module is enabled.

If it's not your own module, use hook_modules_enabled():

Perform necessary actions after modules are enabled.
This function differs from hook_enable() in that it gives all other modules a chance to perform actions when modules are enabled, whereas hook_enable() is only called on the module actually being enabled. See module_enable() for a detailed description of the order in which install and enable hooks are invoked.