I tried working from home with my 6 year old for a week. It was impossible. I lasted 3 short days before I called my boss and said I couldn't do it.
I think it does really depend on your job, it's flexibility and your child's nature. Also I think you'd have to get agreement from your boss - unless you are the boss of course!
My 6 year old was very needy, I could get a Max of 30mins peace before getting 'mum, mum, mum...' again. If left him on sofa with a film he wet himself because he got so engrossed he'd forgot. Bedtime was absolute nightmare because he'd literately not left the sofa all day.
Assuming a desk based/laptop job:
Where will you work? Lounge, kitchen table, office space? If young DC you'd need to be be in the same room as them. I wouldn't leave a small child in a room unsupervised for more than a few minutes.
Will it be noisy - TV, computer games etc? What will they do? Are they good at playing independently? Are you concerned if they spend 6 hours straight watching TV/ computer games? Can they change channel/games by themselves? Do they remember to snack, drink, go to the toilet if left of the sofa watching TV etc?
Do you have meetings/ phone calls? Are they at planned times or spontaneous? Will the kids make noise, try to join in etc?
DS is now 8 and I can work a couple of hours or so from home quite easily, if I've got no meetings planned. If he is playing computer games. If I feed him and tell him to go for a wee before I leave him in lounge and I go and work in office space in next room. But wouldn't do all day. And definitely not a whole week!
Can you do some play date swaps with other parents? One parent has all kids one day, other parent has the kids the next day. Reduce the amount of time off and holiday clubs needed. But personally I'd factor in the cost of holiday club for most days!