Hi,
Probably the easiest approach is to park at Diamantina Hut near Mt. Hotham, and walk the Razorback ridge to Feathertop out and back. No major climbs or descents. It's exposed ridge for the most part, so good weather is important.
It's a 10km walk, so probably 4 hours. There's only 1 or two slightly tricky bits near Champion Spur if I recall, but nothing that will stop kids.
Parking is a bit tricky on busy days, but basically, get car off road as far as possible so traffic can pass, and point it downhill seems to be the advice. I've left the car on the side of the road, a few hundred meters uphill of Diamantina Hut on the side of road, because the Razorback is pretty popular, and it was still there and untouched next days. I took my eldest back in '21 this way, camped at Fed. Hut. I think he was 11 then.
Next easiest start at Harrietville and walk up the Bungalow Spur. You're below the tree line until you hit Fed. Hut, the main camping area near Feathertop, so less to worry about if a bit windy/light rain.
This is about 9km, and takes about 4 hours, depending on fitness. It's a 1100m climb, but never super steep. I dragged the eldest up this way in '20, (he was 10 then) he complained a bit, but only because he wasn't in the mood, was never hard for him (well, he's still alive, so I presume it wasn't that hard).
Parking is at a lot that's been set aside near the trailhead to stop people from parking at the trail head. I've been up the mountain a few times this way and camped at Fed. Hut.
After that, the approaches become tests in endurance I think.
Water might be an issue at that time or year. There's a tank at Fed. Hut, but depending on recent rain might not be reliable. There's a spring on the Tom Kneen/NW Spur track between Fed. Hut and MUMC Hut.
There's also a spring on the way up Bungalow Spur, near the old Bungalow Hut ruins. If you're starting at Diamantina Hut/Hotham, pack plenty of water, as even at altitude, it might be cooler but it's still thirsty work. Maybe check in the days beforehand how the water situation is on this forum or keep an eye on how much rain there's been in the weeks leading up.
There are other camping spots near the summit. The junction of Bungalow Spur track and Razorback track has some spots in the vicinity. There's camping on the top of Diamantina Spur, but it's a kilometer or so from Fed. Hut. You pass the turnoff walking the Razorback track. You can also camp about a kilometer below Fed. Hut at old Bungalow Hut ruins.

- Bungalow Spur

- Razorback / Feathertop