Hello there, and welcome.
In my experience, most of the people on this site prefer long stories that are completely finished, rather than broken into chapters. I have seen a few exceptions to this rule, but in all of these cases, each installment in the story was 25,000+ words long. If you really want to receive feedback before publishing, you could consider setting your story to 'sneak preview' mode and posting a link in the forums. Just make sure that you've revised / edited it in advance.
As for your idea - generally speaking, I think people should feel free to write whatever they want. Writing is a process of self-expression in which you are trying to convey your own thoughts and ideas, not those of someone else. Even though the idea is a bit unusual, I think it could still be great if it's well-written. That being said, I have a bit of difficulty envisioning how a serious story where a toddler is present would work. There have been films and other creative works revolving around a similar theme, where a young child is in a position of power (think of the popular children's movie 'Boss Baby'), but those were comedies.
I suppose it could work if you interwove both silly/humorous and serious elements in your story. A more serious explanation could work if it's more well-thought out than just 'America thought to elect this child as President because why not.' For example, you might consider an adult with a hidden disability which has caused them to regress to the mental age of a toddler. (This still brings up the major problem of how they got elected in the first place). Perhaps you've already come up with a better explanation. To me, I think the best option would be to have the story full-on embrace the silliness of a toddler being elected as President. There have been lots of well-done stories on this site that have included such silly elements, even going so far as to comment on the strangeness of them - which can make for an interesting meta-narrative.
Either way, I wish you best of luck with your creative endeavors.