Feathers and straw both present problems. Even if you use a very heavy ticking they will work their way through the ticking and become a sticking you while you sleep problem. Straw breaks down quicker than the feathers though so it would have to be replaced often. The straw will also create a dust problem because it quickly breaks down and turns to dust. (think about hay and straw you use for your animals bedding and how it looks after they sleep and trample on it for a couple of days). So if your daughter already has allergies this might not be the best option.
Goose down is good even though over time it breaks down as well. It provides greater loft for a longer time than either the feathers or the straw. But unless you have geese to harvest from its expensive. It also takes a lot of goose down to fill a mattress. If the mattress is used only for normal sleep activity it should last for maybe a year depending on size and weight of person sleeping on the mattress and how often it is fluffed up. As it breaks down you can add more instead of replacing. But over time you will also get dust issues.
Thistle down is also hypoallergenic and like goose down provides good loft. Unlike goose down you can gather it from the side of the road when the the thistles bloom. Of course you will need boots and gloves because its a prickly job. But its free, hypoallergenic and readily available. Also something that will have to be replaced and added to as the mattress is used.
Cotton mattress are lumpy and uncomfortable but are also an option.
Anyone remember your parents getting really upset over you sitting on the bed. That was a major no-no in my house. The reason was simple. When people made their own mattresses it was a major undertaking. It required lots of resources and time to make a mattress that was reasonably comfortable for a short period of time. The bed was used for sleep only. No one was allowed to sit on the bed because it broke down what ever was used to make the mattress. Which meant that it would have to be refilled quicker which meant more hard work.
Am I glad I know how to make a mattress out of different materials. Sure. Do I want to make my own? No. Somethings are just better purchased if you have the resources. If you have allergy issues in your house just also purchase one of those hypoallergenic mattress covers. New may not always be better but sometimes it is. And with mattresses, new is the way to go in my book.