What are the spec of your current computer?
If you are using a Duo2Core cpu, expect at least 200% speed gain for the i5, i7.
Im on a pc right now and dont use Final Cut Pro but as I'm a Motion Designer, I often have to edit HD footage. The big bottleneck in editing is the HDD speed. Then the CPU, the ram and the GPU. I dont think Apple products use the GPU cuda cores like Premiere Pro with the mercury engine. I would not worry too much about the GPU.
The mini in itself is not a bad machine. I think your problem now is that you use the USB 2.0 drive as your footage pool. It's slow. Very slow.
If you buy a new machine but keep using your usb drive, I guess you will not see much improvement. Forget about gigabit Ethernet as it is even slower in real-life testing.
http://www.sheldmandu.com/sbs2008/gigabit-ethernet-vs-usb-2-0-transfer-speed-performance
One solution would be to get the mini and replace the internal HDD for a faster 7200 rpm drive. You can put 2 HDD in the 2011 mini with a bit of work.
Solution 2 would be to get a new computer after the refresh at it will have USB 3 like most pc already have.
Also you can tweek your workflow. Did you try other codecs that HVCHD? H264 is really a bitch on the cpu. Better go with some less intensive codecs like ProRes 422 or even quicktime Photo Jpeg at 85% quality...
Edit; do you have a firewire 800 port on your MBP? That would also be faster by a fair bit... 800mps vs 480mps for the usb2... That would decrease your render time quite a bit.