Hi,
There is no option to send a shipping invoice in this plugin. There is however an option to override the shipping invoice. When you activate that option, you will get a PDF shipping invoice when you click on the "shipping invoice" button of an order in the backend order details page instead of a HTML shipping invoice.
So unfortunately, there is no option to send an email with a shipping invoice. Doing that would require some development work.
Now, regarding the invoice, since it's attached to the order status notification email sent to the customer when the order is confirmed, you can add your email address to the BCC field of that order status notification via the menu System>Emails to get a copy.