Filming question: What is the simplest, DIY method to stabilise a top shot ?

So I’m going to be filming a little girl drawing on Friday, and we want to do a top-down shot of her drawing, not unlike those here at RSA animate, so that her drawing takes up the whole screen. Unlike the ones there at RSA animate, I don’t need to pan around—it’ll just be a single shot.

I have a normal tripod, but it’s going to be tricky as it’s a top-down shot, but I need to stablise it so it doesn’t shake. What’s the best way to do this? Should I try to elevate her drawing surface so she’s drawing at a slight angle? (I don’t want to inconvenience her too much). The less equipment the better, as we’re not shooting in a studio (and may even be shooting in a park!)

I also have an iphone that shoots HD, so that’s also an option (will be lighter if I’m making a DIY tripod)...