I think it's worth considering what you see as the benefits of home ed.
Go and visit the school(s) that you would look at locally. And spend some time with some local home educating families to see what their real days are like. Also I'd start whatever application processes you need to (if you can turn down a place later) as it's easier to keep options open as long as possible.
I was very, very taken with the idea of home ed when DS1, now 14, was very small (around 1-2 years old). To me at this time, it felt like a continuum of what we had been doing which was very lovely, attachment parenting, lots of social groups - breastfeeding support, sling meet, parks, children's centres, library, exploring, museums, playing, I just never wanted it to end and home ed felt like a way that I could do that. But something that I hadn't really considered at the time is that things would change - he would change, I would change, our relationship would change. It was hard to see anything different to that lovely close toddler stage which I absolutely adored (and went on to have two more children several years later, so I got to do it all over again) but the later stages are different and that is OK.
I was also lapping up a lot of the home ed narrative which is that schools are really conformist, they have only one way to be, they only support kids who fit perfectly in a "normal" box, the behaviour management systems are coercive and broken, etc etc etc. Which yes, there are grains of truth but it's in no way the full story.
OTOH, I wanted to go back to uni (which I did when he was 2) and work towards a career for myself. I loved the idea of being a SAHM and I didn't want to rush him into school/childcare ASAP but I also wanted that experience for myself in life. I was pretty young when I had my first (I wonder if you are too, since you refer to career in the future tense and only study, not work, in the past tense).
I ended up signing him up for the free nursery place that he was allocated at 3 years and it was the best thing. I was starting to struggle with the SAHM role (even mixed with part time study) and honestly we just did so much better with some extra space from each other. It was also around this time that I realised despite being totally in love with the ethos of home ed, I would be crap at it. In order to home educate well, I think you need to be a pretty determined and active person yourself. I'm not - when I'm at home with DC I tend to default to letting them play or watch TV while I go on my computer. There are occasional learning moments but everyone jumping in the car (not that I even have a car or driving licence) and going out to explore an interest is exhausting and not something that comes naturally to me at all, no matter how much I want to be that person. I do much better with a schedule that is set by somebody else, or I tend to default to ennui. If I had done home ed I might have been fine if I'd joined all the groups, but I still think this probably would have drained my energy so that I barely had any left for fitting things in in-between. Whereas if you're more enthusiastic and more likely to jump into everything then it can be a really rich, stimulating environment.
I looked into schools and found out that the school attached to his nursery was lovely - nothing like the horror stories. It also brought back some happy memories of my own school years. They also had some really great innovative stuff like Write Dance. I came to realise (several years later) that a lot of HEer's views of school are outdated, based mainly on their own experiences, but also, not by any means the norm. There's a huge amount of neurodiversity in the HE community, (both children and parents) which can make it feel incredibly welcoming and fitting if that is also you, but it also tends to predispose them to have poor experiences with schools, and so these experiences do not reflect what the majority experience, even though if you're mainly hanging out in HE-supportive spaces, it can feel like the majority experience. Bear in mind also that a significant proportion of HEers have come to that path because they have had bad experiences with schools. But again, that won't be everyone's experience of school. In fact, most kids get on pretty well at school. The right school, with the right staff, can have a lot of the same benefits as HE. There are definitely downsides and you will absolutely come up against teachers, classmates, subjects or situations which aren't as easy as others but most of these things are temporary and there are upsides to a school route which often cancel these out (not for everyone).
If you want to follow your own interests and encourage your DD in following hers, you can do this outside of school hours, during holidays, weekends etc. It's not like HE kids learn 24/7 and kids at school just shut off their learning when they are at home. Yes it's not the same, as you won't have unlimited time and you will be expending a certain amount of energy on all the logistics of school, work, commuting, homework etc. (Bear in mind that you following your interest to that end point of work will also be a really valuable model for her).
To some people, the freedom of HE is exciting and inspiring whereas others find it daunting. I know one family with ADHD where they genuinely cite the lack of a school run as reducing a significant amount of stress in their lives because mornings are so challenging for them.
You mentioned finances factoring into this decision. You may wish to run up some rough budgets including: Pre-school childcare, wraparound care for school age, holiday care, school lunches, costs involved with HE groups, costs for HE materials, subscriptions to any learning services that you want to use, a budget for trips/outings, and ideas of what kinds of things you might be able to afford in terms of lifestyle with/without work/with PT work/etc.
You might want to look at local private schools. If that makes you instantly recoil, just look. Yes, some of them are overtly classist and elitist and may not be a fit. But there are often schools which have a more holistic approach. Since finances are something in your equation, it seems silly to ignore this - it might not be suitable but it might be worth looking.
Sorry this ended up a bit scattered - hope it came across OK.