It's good to treat homeschooling as a major undertaking and to be cautious about it. It isn't for everyone. It wasn't for us, the first time we tried it. And it may not be for us this time, either.
Most homeschoolers I know have slipped behind national standards in Australia. We're going to use a curriculum, Sonlight. It's Christian but the science and maths components are secular. It's just that the English literature component includes Bible study. They offer a completely secular alternative, BookShark - but BookShark doesn't ship to Singapore.
Two months is a great amount of time to budget. We had much less, because the background checks took so long. The team were desperate to have my husband on the floor working though, and he really wanted the job. So he gave the mobility team a date about six weeks away and they booked the flights. But it wasn't confirmed until three weeks before our departure. So we had three weeks to pack up the house and relocate, which was in my opinion stupid and ridiculous, and now we're here in this situation.
Don't do that to your wife and child!!!
I would suck up the cost of having things packed professionally, too. We did that when we moved from New Zealand to Australia - because we had a 1 week old newborn (we moved when he was 2 weeks old. Yeah...I've been through too much of this already!!). It was so much easier.
This time we tried to do everything ourselves and put everything in storage and used it as an opportunity to declutter, so freecycled and sold a lot of stuff, and with only three weeks it was just a debacle to be honest. I wish we'd just hired people to pack everything, even the crap we didn't really want (like they did the last time) and saved ourselves the stress.
In retrospect I would have demanded that the flights be booked after the the background checks were complete. Little things can make the process drag on. For my husband, they needed confirmation from a particular line manager he had, who had since moved on to a different company and relocated to New York and was very difficult to contact.
How old is your child? Mine are at a reasonable age to homeschool because they're 11 and 8, and can already read and write confidently, so they can make their own way through workbooks and worksheets, etc. They're also boffins by nature - at the moment, even though I don't require them to do anything, the 11 year old is working on a children's picture book that he's written, and the 8 year old is creating a Diary of Singapore Adventures journal.
At kindy/grade 1 age, it's much harder, because you're teaching a child to read, and teaching basic facts in maths, like numbers and addition/subtraction. Mine are well over all of that now and also better able to deal with the frustrations of learning.
It does offer some amazing opportunities. I think I will give them each a 'passion project' for the year, something to research and learn a lot about - they can choose anything they want. One might choose Ancient Greek gods and goddesses, and the other might choose medical machinery - those are their interests off the top of my head. As a reward at the end of the year, I could give them an overseas trip to something relevant to their project. I think that would be a really memorable learning experience, and something that can't be replicated in an institutional setting. It might make up for all the socialising they're going to miss out on by being at home.