I just moved with 3 kids. I had about 6 weeks notice, and it felt like loads of time. It's not! 
Work out how you're going to move - my last house move I used movers, but they quoted me a huge price this time so I used a local man&van company - they were great, loads cheaper and despite the multiple journeys actually took half the time that the removal company quoted 
whichever you choose, book it with plenty of time to spare and keep the money aside.
Start packing now. Pack anything you won't need before you move - things like pictures/ornaments, books, DVDs, kitchen things you only use occasionally. If your kids are at nursery or school, use this time to pack without interruptions. Label the boxes clearly with what's inside and which room you want them in.
Take the opportunity to get rid of anything you don't need - my previous move had been done with very limited time so I ended up just chucking stuff indiscriminately into boxes, meaning I had a garage full of boxes I hadn't even opened in the 2 years I lived there 
I went through each box and I got rid of absolutely loads of stuff, a lot of it old paperwork and stuff, which was great because I was downsizing. There are sites online that will buy CDs, DVDs and computer/consoles games in bulk off you rather than having to waste time listing on ebay or just give them away (really handy for me because my ex had left loads of stuff behind), and also some that will buy clothes by weight. This meant a bit of extra money coming in too For large stuff see if your council has a bulky uplift service - mine offers 3 free uplifts per year, and additional ones for £15. I did still bring a couple of "misc" boxes, but it was much more manageable than last time.
Make sure you pack anything you'll need immediately - kettle, tea bags, loo roll, nappies/baby wipes etc - in a separate, clearly labelled box.
Get as much help as you can for the day itself. If possible get the kids to stay somewhere else the night before - aside from the ability to move child free it means you can pack their bedrooms the night before and they'll have their special things with them so you won't need to worry about finding them in amongst everything else
Prioritise once you've moved in - the only thing that you need for the first night is somewhere for you all to sleep so focus on clearing enough space in the bedrooms and reassembling beds if needed
Plan something very simple for tea or if you can afford it order a pizza or something. You won't be able to see your kitchen for boxes
Good luck! Lone parenting is very good at getting you out of your comfort zone and becoming much more self-reliant, I'm sure you'll be absolutely fine.