It's speculation of course, but I sense it goes something like this:
Forest is usually the subconscious. Pool in the depth of the forest then is a gateway into the other side.
The chain is difficult. Could be her heart - lost her heart - but it's a chain and a gift from her mother at birth. Obviously she didn't head the advice to watch it carefully. And then the Elk, who I see as her double (at home in the forest), told her it wasn't everything. So its some kind of longing, but not her real heart. Precious nonetheless.
Some kind of talisman from her 'mother' at her 'birth', which could equate to her soul. It had such a hold on her though, that she couldn't leave. And yet it appears it was something in the pool which had the hold, more than the heart chain.
You'd have to think the heart chain was some kind of emotional love. Not within her, but a kind of attachment she valued, and quite likely, if she had of cared for it carefully, may have protected her from the power of the pool.
I also feel the pool is not evil in itself, but that it has a natural power which has to be resisted, or what lies within the pool.
In the end, I'd have to say the princess lost her soul to the astral world, through not being prudent and listening to her double's warnings. It seems much like the warning DJ gave about the dangers for dreamers.
But then, the Elk seemed to feel that the pool could save her from the dangers of the forest, including 'loss of innocence'. Thus it was a kind of gamble on the Elk's part, which alas...