Hi Kambonas,
Since you are moving to a bigger city like Dar, then you won't have any trouble buying things that you need. There are lots of stores that sell appliances, pots, pans, etc. Just be prepared to pay a bigger price for them. A single frying pan can cost you $20-30 usd. (new) But there are often expats moving and selling their things. What ever you have as your set up cost budget, double it, or triple it. Things add up very fast, electricity converters, fans, plug in heater, mosquito nets,trash cans, etc. It gets expensive quick.
You can also get a generator here but again expect to pay more, but it might be worth just getting one here if you would have to pay a shipping cost on one.
The one thing that I would recommend focusing on bringing is kids things. We have 3 ourselves - Ages 4,3, and 1. They have children's things here but they are usually not good quality, falling apart very easy, and are very expensive.
The things that I would recommend is a portable high chair, do they have Wal-Mart in Australia? I can recommend a great chair that we use. Restaurants here hardly never have high chairs, and we take ours everywhere, and just strap it on a chair in the dinning room at home. Also a portable play pen, this would count as a luggage piece, but it might be worth bringing if you already use something like this at home. A stroller is also something to think about. We used this at the airport, they took it at the terminal gate, they put in under the plane, and had it ready for us at the next place. So in other words, it doesn't count as luggage. I also use mine a lot around the house and when we go some places.
Also baby food can be $4 usd for one little jar, I have learned how to make my own from scratch. Diapers and wipes are more expensive. Might consider bringing good quality cloth diapers.
You can get used doll type toys at the market, really used, but cheap. Electronic or "cool" older kid toys are Very expensive.
There are pharmacies Everywhere, so I wouldn't worry to much about a big first aid kit, although having things handy for travel is nice. You can get medications for kids, like liquid Tylenol/Motrin, which the call Paracetamol. But things like "melt away" medicines, they don't have, also things like burn patches (which i have seen in America).
You can email me at EastAfricaMisions@me.com and I can email you my mini book on moving here. It gives some information about budget things, malaria, etc. Also I also have two blogs, eastafricamissions.org and mamaTEMBO.org
Take Care,
Bonnie TZ