A big warm welcome to the comunity :-).
Not having a 'real' Amiga is not much of a handicap if you want to start experimenting with the AmigaOS. The EEEPC is reported to be able to run some flavour of UAE and thus should be able to let you start playing around a bit.
However, keep in mind that the UAE emulation does not exactly copy the feel of a true Amiga. I know, some might think I'm contradicting myself as I once said that UAE does a good job in emulating the Amiga, but only a few weeks ago I noticed how it smelled at running OctaMed ;-).
But for now, buy yourself the latest version of Cloanto's Amiga Forever and start playing. When you like it, start screening eBay for a nice, real Amiga ;-)