And once you get the 10.5 DVD, install the free 10.5.8 update. Note, once you have installed 10.5, you will lose access to Classic. If your Mac can boot Mac OS 9, you can still do that, or you can partition your hard drive after backing it up to a Firewire hard drive to have both 10.4.11/Classic and have 10.5.8 on separate partitions.
Carbon Copy Cloner and Superduper have older PowerPC versions you can use to make clones.
The highest all eMacs can go to is Leopard 10.5.8. Like the others said, an install CD set is the only way to do this, I don't know if apple has them anymore but they usually go for around $60 online and eBay. Once you upgrade to 10.5.8, you can run safari 5.0.6, which lets you do almost anything online. Or on the other hand, for the $60 you'd spend on a CD set you could probably buy another used mac online which already has 10.5.8 for almost the same price.