You are correct, the shipping information does not import with the product. However, this is because the shipping is different per product and different depending on where you are shipping to. This is why it was never included in the import list!
For shipping, you will need to set it up manually in Shopify. This does not mean you need to go through and copy every single shipping method. Actually, that would not work because it may change depending on the country it is going to! What we suggest is averaging out the shipping and using one price. Or, add that into the product mark-up and then offer free shipping.
I will give you an example based off a previous store of mine. You are selling t-shirts and watches. Let's say each is priced on your store for $10. The shipping of the watches is around $1 and for the shirts is $3 on average. So for shipping in Shopify you'd put free shipping. However, you don't want to lose money so you'll take the average of those shipping costs ($1+$3/2) and add $2 to the price of the watches and t-shirt. Instead of $10 you will now charge $12 for them to make up for the illusion of free shipping in Shopify.
I hope that helps! Here is a guide to setting up shipping in Shopify step-by-step. This might be easier to follow. Let me know if you have any questions!