You can find the Ubercart invoice email template files @ sites/all/modules/ubercart/uc_order/templates. You could copy and edit the uc-order–customer.tpl.php to fit your needs but you could not select it @ E-mail customer checkout notification > Email an order invoice in Rules. This is because you have to implement the hook_uc_invoice_templates() before the new template is selectable.
Luckily, there is a module called Ubercart Register Invoice Templates which simplifies the setup.
2. Copy the /sites/all/modules/ubercart/uc_order/templates/uc-order–customer.tpl.php to your theme templates directory. Rename it to uc-order–<template-name>.tpl.php and make any changes.