In your form, I'm assuming you have a submit data connection that submits via email. Is that correct?
This Office Online page, in the 6th step of the first section, is describing what I'm talking about. Basically, you need to select the email connection from the data connections window, and set it to include the form as an attachment. If you'd like help with this, you can attach your form to a reply, under the Options tab. Or tell me what version of InfoPath you are using, and I can provide steps.