When I first started trauma therapy I thought it would be for 2 or 3 months. When I found out the centre allowed a year, it was a shock. It's really hard to get your head round something like that. I understand it now, although it was very unexpected to me at the time.
I've just had nearly a year off work due to overwhelm, and while it was very hard financially and it made me worry, everything turned out OK. I don't know about where you are, but it's so common here (the UK) for people to take time out for personal projects, travelling, family, creativity or whatever reason that no-one was bothered about my time off work when I started applying for jobs.
I would be asked, and I always said I'd wanted off time to renovate my house and garden, and no-one bothered to ask any more. (I was ready with something more specific to say if they had asked.) I know yours might become a longer timeframe, but then I think it's just a reason that has a longer timeframe. If your anti-discrimination laws are anything like ours, wanting to spend more time with your child/children would be a reason that would probably go unquestioned.
I understand that money can be a serious concern. I don't know your situation, but I also wonder about studying, for financial reasons as much as anything else. Putting everything back a year, including studying, might be a good idea if this is what you need in order to heal.
I don't know if taking a job that wouldn't be the usual kind of thing you'd look for, but is doable and doesn't put too much pressure on you is a possibility for a while?