Imagine that the universe contains the world as we know it, and somewhere, very far away, it contains heaven. Now imagine a line between them. The author is saying that on this side of that line, Donna is the best thing. On the other side of that line, maybe there is something better.
More generally, “this side of” is short for “on this side of some boundary.” It makes literal sense in phrases like:
the meanest hombre this side of the Pecos
since the Pecos is a river, which is a natural boundary, or even:
There is no safety this side of the grave. [Robert Heinlein]
if you think of the grave as a boundary between real life and the afterlife.
But it gets used a little more loosely, with large or shapeless things like “heaven” or “paradise” or “happiness” rather than an explicitly named boundary.