There is a WooCommerce feature called "Product Variations" that allows the customer to specify attributes of a product (ex: tshirt size or color), which can have different prices. You can also use the Gravity Forms WordPress plugin with WooCommerce to make fancier integrated forms if you need to.
However, this all requires that the base product be in the WooCommerce database already. Could you perhaps have a super-basic generic Woo product to hang this off of?
If you truly need to generate Woo products on-the-fly, I don't know of an extension that does that, although there could be one. You might need custom code to achieve what you are after.
Good luck!