My laptop is HP pavilion g6 series
Yes, any of the socket FS1 (Llano) APUs should be compatible. Keep in mind that your A4-3300M is specified for 35W TDP, and some of the higher-performing APUs have 45W TDP - and thus will likely run a few degrees hotter in your notebook.
You should not expect a large increase in performance, and I would not recommend spending a lot to upgrade a 2011 notebook. The main decision is whether to get a faster dual core, such as A4-3330MX (that's from 1.9 GHz to 2.3 GHz); or a quad core such as A8-3530MX (that's still 1.9 GHz, but 4 cores, and slightly better graphics).
