When my brother (a very keen walker) tried this for the first time, he came back and said that it was a LOT harder than initially anticipated, and he would probably never do it again, but would rather camp somewhere where they could do day trips.
I ignored this advice, and have taken our kids on a couple of trips while very young, but found he was right. It ended up being a LOT harder than I was initially expecting.
Thankfully I listened enough to make sure I only did a VERY easy walk. We've now done this same walk with our two kids twice.
Some details and photos of the first trip are here. And...
The trip report for the second walk is here.
The first time, we had to carry both kids, being only 2 years and 4 months old. This made carrying anything else very difficult. My wife carried both kids in, the eldest on her back, and the youngest on her front. I carried two full packs in. On the way out, we took a child and a pack each. This was back breaking and heart breaking work (and the rain didn't help), even for such a short walk. About 3/4 of the way there, I dropped the packs, and helped the wife with the kids the rest of the way, and then went back for the packs.
The second time, we were aware of the issues, and did it differently. The eldest (then 3) walked all the way, my wife carried the youngest, and I carried just 1 large pack. I then went back to the car for the second large pack. Being a very short walk made the second trip for the second load possible.
The first trip involved a lot more nappies, and such (with both the kids very young), but the second trip required us to take our light weight portable cot, which was quite bulky (and not all that light). For both trips, we stayed in a well equipped hut and did NOT carry tents, stoves, crockery or cutlery. But we still needed double carrying capacity for all the kids and the extra gear kids require. Carrying out 6 kid-days worth of dirty nappies is substantial too.
Baby carrier back packs are VERY uncomfortable after some time. I've tried a few, and they simply cannot be made as comfortable as a normal bushwalking back pack. You will get very sore carrying one for any significant time.
I would recommend doing only an exceptionally short walk (what would normally be a very short day walk), but do it as an overnighter. Allow for two trips for all the extra gear if you're not absolutely certain you can carry it all at once (and so long as there's enough people to stay with the kids!).
IMPORTANT TIP: We planned our walks well ahead of time, and started collecting the Huggies Baby Wipes bags. These are large plastic zip-lock bags, and quite tough. You can fit a LOT of dirty nappies into one of these when you really squash them in.
PS. ONE MORE TIP: My wife's fleece-lined down-filled jacket made an excellent sleeping back for the 4 month old.