Arduino Due for camera control?
You are still not giving the full picture, pun intended.

I'll give you an example of what sort of info is missing.

For example, what's the frame rate? What's the color depth of the sensor?
If you look at the SAM3x TRM, it says that the SPI is clocked at max 65MHz.

So, the (simplified) math would say: 

24bit/pixel * 5Mpixel / 65MHz =  1.846 seconds

And that doesn't even account for acquisition time, so if you do not have fully working DMA on both sides, it's probably even worse.
And it will be worse, because you cannot stuff in RAM in one go the entire image.

But maybe that's good enough for you, however it's not possible to say because of the missing info.