I am hoping to begin making my cutter today. You should really search the forum for curd cutters, there are a lot of pictures, ideas, and considerations.
Here are a few things to consider:
You do not want too small of a dowel that the tension of the wire would start to bend it.
I ordered SS trolling line from Cabela's I think I got the .18 size. It was $8-ish for 230ft.
How will you attach the wires, consider if you tie them, for example, the risk of bacteria growing in the crevices of ties.
The consensus here seems to be that putting a grid of wires (as opposed to just one direction) in one cutter is not good as it will be too much resistance pulling against the curds. I personally think it might be okay, depending on the cutter and the wire gauge.
Also, if the cutter pictured above is the only one your going to make, remember all you will get with that is like cubic rings that go around inside of the pot. From there you can cut it with a curd knife but it will be difficult to get super-even cubes because you are cutting into a bunch of rings. I hope that makes sense.
Maybe I will have a picture of my setup soon, assuming it pans out. It is going to be two pieces, one that pushes straight down into the pot and cuts columns of curds, and another to spin on the inside to cut the levels.
But I really suggest reading all the posts about curd cutters.