A Raspberry Pi might be able to handle it. But a Raspberry Pi runs a multitasking OS, and when you have multitasking you need buffers and buffers are a delay (latency).
It also depends on the amount of data... i.e. The number of channels, sample-rate, and bit-depth. And of course the complexity of the processing. The only you're doing that's complex is the EQ.
Rack mount audio processors are usually built around special-purpose DSP chips.
If you've never done any DSP programming before, there is a good [u]online DSP book[/u]. And for things like filters, you can find libraries so you don't have to write the code from scratch.