As soon as the payment goes through, you will automatically receive your invoice per email. You can also download your invoice directly from your account settings under your the "subscription" section here:
www.doodle.com/settings/subscription
If you are renewing a subscription, the invoice will not be generated until the old subscription runs out, and the new subscription (the renewal) begins. You will also not be charged for the new subscription until the old subscription runs out. On that date, the invoice can be accessed as described above.