This isn't a good idea to plan to do on your own; there's a reason that most workplaces specifically don't allow employees to work from home while concurrently looking after children.
If you're a business analyst, I'd imagine you'd need to be quite focussed on working through the requirements of your organisation, possibly thinking about how to weave processes and systems together, writing reports and perhaps a bit of project planning.
All that work needs concentration, which means you'd have to ignore your baby for stretches of time. Most children when ignored cry harder, you'd be unlikely to be able to sustain that for long.
You also need to think about other practicalities; what happens when someone wants a 5 minute catch up in 10 minutes, but baby needs feeding? What happens when you are on a call and baby suddenly starts wailing? For those reasons and many more, you need to arrange proper childcare while working.
My DH and I are working from home during this crisis with DS3.5 and DD2.5 (she also has SEN). The only way we are able to do this is because we arrange our day in shifts, one person working, one person solely looking after the children. When nursery starts up again, they're going back!