I was riding to school in grade one that corresponds to 5 years old by myself.
This was considered young by many people.
Traffic was different then.
How well your child's road sense and appreciation of the risk involved is developed would need to be considered.
I think it is important to get a bike that fits the child.
If the cost of replacing bikes regularly (18 to 24 months) is an issue there is often a good range of kids bikes at the bike workshop.
Bec, formerly of Adelaide and now in Vic bought her child a good road bike more than a year ago, it might be worth PMing her direct for opinions, given how quickly kids grow it might even be for sale before long
Minimum age is 12 for the velodrome - certainly the one at Jepps Cross. Nathan wanted to have a go but he's only 5, so he'll have to wait :-(
My son is only 7. He's got a road bike and does 60-70 km with me most Sundays. Biggest ride is 100. When we were looking around for bikes for him we settled on the Avanti Giro 650. It's about the best around. It has some really nice touches like concealed cabling etc. Only criticism is the wheels are a bit ordinary. They seem to have non-stainless spokes: For Heaven's sake!! He uses Keo easy pedals/cleats.
He's probably done a couple of thousand ks on it so far and it's running well. Don't forget to get a rear dérailleur guard and wrap the brake gear levers in insulation tape.
Our son is almost 6 and has been into BMX out at the cross keys BMX track for a few months. They have a good juniors program and you can use their bikes.
Another option we looked at was a bit like the velodrome is Cycle Speedway (Skid Kids) I have heard this is also a great way to get kids riding/racing
Bugga the kids, the Skids Kids are great fun for adults too - I did it with my son. You used to able to just rock up and try it. Great fun and well organised. We didn't keep it up because the boy wanted to kick a poor, defenceless ball around.