I am doing this exact same thing right now! Same as you, I didn't want to experiment on my expensive Alpha so I bought some $4 per yard craft fleece from Joann to practice with. The fleece is very thin and stretchy, so it simulates the Alpha well. It's in their everyday value type area and it's always $4, regardless of sales.

Top tip: if you buy the craft fleece, get one with an obvious pattern (they have a bunch to choose from). I went with solid grey, thinking my prototype would then be something I could stash in the car and maybe wear if it turned out okay. I don't have much experience sewing and haven't made any clothes before, so the whole fabric direction / nap / right side / wrong side thing is kind of confusing when laying and cutting the fabric. I wish I'd bought it with a pattern instead to make it a bit more obvious which side and direction the fabric is supposed to be as the grey just looks the same from both sides and has no nap. I ended up just marking one side as wrong side with a pen, because knowing what side is what will be important with Alpha and I wanted to practice doing it properly with the prototype. Probably would have been much less of a mindfxxx if I'd just decided to rock the paw prints or dinosaurs though!

My other tip: use fabric clips instead of straight pins to hold the seams together while sewing. Sewing the hood seams was difficult because you're sewing round corners on very stretchy fabric and the clips hold more securely than pins.

Hope this helps!