Wait, if Zoe is truly the "messenger"/"herald"/"whatever" of Targon...
... then maybe the moonstone she carries IS actually the one that's supposed to go to the Marai in exchange for the abyssal pearl?
As to why Zoe does not do it... my guess is she simply forgot why she was here. She teleported into Runeterra, saw a butterfly, and got distracted, completly forgetting about her objective.
There IS another possibility however: is it certain that Zoe has truly ALWAYS been a child? Given that she's pretty much a living god, I'd assume that her appearance is vastly depending on her mental state. The questions now are: a) was she different before? and b) what made her change into this state of mind if she was truly different before? I mean, what would you get from giving up your adult mind for that of a child?
Actually, there is quite something to get. For example the power of denial. If you are a kid you don't have to really do anything, and you have zero responsibilities. And as for the horrid complexities of the universe with all it's contradictions... you can just pretend it doesn't exist because the world around you is too exciting for you to have a quiet minute to think about it.
Now we got some possibilities:
She's denying
a) something she does not want to deal with,
b) something can't deal with
c) something she could deal with but it would trigger a chain of events that would bring disasterous events over the entire universe and it would be her fault, and she's not having that even if it was needed to save the universe from the Void or something.
Or this option:
d) she encountered something so traumatizing that she reverted to her child-like self in an attempt to protect her sanity. Given that Targon directly deals with the Void, and that Targon seems to be in some sort of crisis themselves, that might not be so unlikely. Not sure how I'd like after getting Malzahar's visions in my brain for some days, but now imagine a god getting tormented by it for a few years or so. Surely not healthy, I tell ya that.
There is also the possibility that this was the intended result. They (possibly the Void or whoever is ruling in there right now) was aware that they couldn't kill a Targonian aspect. HOWEVER, it was enough to drive a specific one insane to the point where it COULD NO LONGER FULFIL ITS DUTIES PROPERLY. And the exchange for the moonstone seemed to be important to keep the Void-Rift under the oceans sealed. Now, maybe if that was the plan after all?
At the same time out of all aspects she's the most fitting target for a void attack. Given that she jumps dimensions, she is closer to the "edge of reality" than others and therefore also closer to the Void.
Oh god I fear for the moment when the void breaks through at the bottom of the sea and Zoe is like "wait, that was my job to prevent that" and the trauma comes breaking up again. I mean, if done right it would be a hyper emotional moment in lore, especially badass if you could have her temporarly transform back to her non-child self (be it adult humanoid or giant space monster or whatever). However, this would also mean putting her through literal hell from a narrative perspective, and I'm not sure if I want that to happy to that lovely brat Q_Q
Or maybe I'm just cooking up weird nonsense at 3 AM? You gotta decide that I guess...