Unibody Macbook vs. Mac Mini for HD video editing

I am currently editing my videos on a uniobdy macbook, I film with a Canon t2i and convert my files to prores 422 for editing. My computer runs fine when I am editing a 2-3 minute cut which translates to 1-2 hours of Final Cut Pro 7 being used. At about 1.5 hours into an editing session I can feel the computer getting bogged down but not to the point where you can't edit, just a little bit slower than the speed it started out in. This year I have decided to produce a 30-40 minute film and I am worried that my computer just won't be able to handle it but I also don't want to buy a brand new laptop seeing that my laptop is fine for everything else just not video editing and I also don't have money to blow on a decked out 15 inch MBP. I have been looking into refurbished MacMinis, I will not be doing any crazy graphics nor will I be performing tons and tons of quick cuts, instead I will just being doing simple titling and editing of HD video. I was wondering what internal parts should take priority in a Macmini for HD video editing, I really don't want to spend anymore than $600 seeing that I really don't need Final cut Pro to be running full speed without flaws for 6+ hours, I just want it to be able to handle 3-4 hour editing sessions without bogging down to the point where I can't use FCP. I know RAM is a pretty big deal along with the graphics card but I would like to know what 1-3 things I should really being looking out for that would make a difference in editing efficency/speed.

Thanks,

Tyler