Hi cw2697,
Post #2 here and the topics it links to also has much more information about mattresses and children and “safe” materials including a link to some general guidelines for children in post #2 here. It also includes a number of links to the better forum posts and topics about mattress and children as well which also include more information about many good options for children which may also be worth considering.
While 3" may be OK for your child … it would probably be too thin for you and most likely wouldn’t be very comfortable for you at all and it may not be as suitable a choice for her either when she gets older and larger. You would probably be better off with something a little thicker if you are looking for something that will last you longer.
If you are looking for some very low cost options that would be suitable for a child then it may be worth considering the Spindle Mattress B stock here or the Arizona Premium children’s mattress here that is made from their “fall off” material.
A mattress cover (ticking), mattress encasements, and mattress protectors are all completely different products that are designed for different purposes. There is more about the differences between them in the last part of post #6 here but since they are different components designed for different purposes I wouldn’t use one as a replacement for another. I would tend to choose a suitable tight fitting mattress cover for the mattress itself and then use a thin “membrane type” of protector that fits like a fitted sheet on top of it that has a waterproof membrane on either the top surface or on five sides and is more easily removed and cleaned.
Post #1 here has more about the different type of support systems that are generally suitable for different types of mattresses and in the case of latex I would use a firm non flexing slatted foundation or a platform bed which has less than 3" of space between the slats (most slats would be 1x3’s which are actually .75" x 2.5") and with a thinner mattress then less spacing would be better yet because you would be much more likely to feel the slats under a thin mattress. If you purchase a foundation or a platform bed where the distance between the slats is too wide or you can feel the slats through the mattress then something like the bed rug here or one of the slat conversions here (which has no flex at all) or even one of the Ikea slatted bed bases here (which has some flex which may change how the mattress feels and performs) or even a vinyl lattice like this could help increase the surface area and improve the support under the mattress and reduce how much you would feel the slats.
While some people may like the idea of sleeping on buckwheat … I personally wouldn’t be one of the people that would try to convince you to try it compared to using latex.
Phoenix