That part won't do the job- you'll need something with cones and a thread (i doubt a kid's bike comes with cartridge bearing hubs).
This is what you need-
http://www.cyclelife.com/Product.aspx?pc=2&pt=23&pg=2207
Yes, it says 145mm (they also do 140mm) but you need some to fit inside the dropouts- so the end of the cones will be 135mm apart, with some extra to fit in the dropout. You'll need to measure your dropout thickness to decide which to go for.
When we fit these to bikes we usually use the cones and bits off the axle already in the hub as there's usually some variation.