Defiantly single core. It's also an older model. N270 CPU and GMA 950 graphics. The newest Compaq mini CQ10 has the N450 CPU and GMA 3150 graphics.
To go from 1GB to 2GB you'll need to remove the 1GB RAM stick and replace it with 2GB stick. There is only 1 RAM slot. The CQ10 has an access slot on the back so its an easy upgrade.
You can find the CQ10 maintenance and service manual here: RAM upgrade on page 38
Check the fine print of your wireless service plan to make sure there isn't a data cap where they charge you a LOT more once you go over what's allowed in your $18.35 monthly plan. Not all wireless plans have this type of 'Gotcha' but if there is you want to know about it up front.