Do I have to provide an invoice for a private sale item if requested after the the item was sold?

[11goodies]

It was of course a second hand item and I am not a commercial dealer.

It was initially local pick up only and the buyer asked for posting it.

The postage was the minimum amount and the buyer has been asking for an invoice because of the postage when all the messages regarding the postage back and forth have been all under ebay account messages inbox..

The buyer says she couldn't make a payment through palpal because it was 'pick up only'. 

I just don't want to do up the invoice. 

I think she is being unreasonable for not making a payment, isn't it?