The most easy part should be checking on the table and then escape it.

public function boot()
    {
        DB::listen(
            function ($query) {
                if (strpos($query->sql, 'querylogtable') !== false ) {
                    // we don't want to log about the logging
                    return;
                }
                QueryLog::create([
                    'sql' => $query->sql,
                    'bindings' => implode(', ', $query->bindings),
                    'time' => $query->time
                ]);
            }
        );
    }

I have used implode and not a foreach to glue the bindings