Heyho there, love! Absolutely, Duolingo is a great way to get started with a new language and to get a feel for it; and yeah, unfortunately, they don't offer Old Norse or even Icelandic.
But first off, it depends on which Old Norse you want to learn. The version I am aiming for is West Old Norse (which then developed into Old Icelandic and Old Norwegian), the one in which the Poetic Edda was written, and East Old Norse (which then developed into Old Danish and Old Swedish). I hope I got that right, haha. West Old Norse is incredibly similar to Icelandic. I would dare compare it to the difference between Modern English and Shakespearean English so if you know one, you almost automatically know the other.
You can use this website to get started and I recently came across this book called "Viking Language 1" by Jesse L. Byock which is now waiting to be studied by me!
I also recommend Jackson Crawford's YouTube channel, he as a lot of videos on Old Norse!
I hope that helps! ♥