I don't really have experience with netplay but my mom's computer which I'm currently doing work for school on (as you can see) has specs close to that laptop in terms of the benchmarks that I saw. The specs:
Processor: i3 550 @ 3.2Ghz
RAM: 4GB
Graphic Card: AMD Radeon HD 5760
I quickly ran melee on fountain of dreams and it runs on 60 fps pretty smoothly. It might probably run even better with the
netplay community build which includes lagless fountain of dreams.
If anything, it'll be your graphics card that would be the limiting factor though I don't know how good the onboard graphics + coprocessor really work. Perhaps look at the
dolphin website for some further guidance.