two options

create a service item which posts to an income account, pre-paid shipping and use that on the customer invoice

or

check gear>settings>company settings>expenses>bills and expenses and turn on make expenses and items billable
check mark to track billable expenses and items as income
then in company settings>advanced>chart of accounts click the edit pencil and select the billable expense income account

Why intuit separated the two related settings is anyone's guess

When you enter a vendor bill/CC charge/etc, you will see a Billable check mark box, check that and select the customer name in the customer block. The next time you invoice your customer, the system will show billable expenses on the right side that you can click the add link to add the bill to the invoice.  IF you do not want to add the bill to the invoice, leave the billable check mark box blank, the cost of the expense will still count against the customer