It's better to say: My poems haven't been written yet, so they are UNWRITTEN POEMS. The letter hasn't been sent yet, so that is an UNSENT LETTER. The poems and the letter are the object of the actions (write and send), so you can't use do.

I agree with Neemias. To add to him, it's important to note the kinds of adjectives and situations where adding "un-" is natural and common. In your case, an "unsent letter" is not something you would use regularly for the status of a letter after you have written it but before you have posted it. It would be good if you had written a very powerful letter to someone important to you, but never sent it for complex reasons, and it was discovered much later. It's the same for "unwritten poems". It's not normally used. Perhaps you could describe all those poems in your heart which you have never had the courage or confidence to put on paper as "unwritten poems". So your examples work well in a literary or dramatic context.