I have taken a much better image of the circumstellar disc now.
Please see the updated image here: http://www.rolfolsenastrophotography.com/Astrophotography/Beta-Pictoris.

This image shows the famous debris disc of debris and dust orbiting the star Beta Pictoris 63.4 light years away. This is a very young system thought to be only around 12 million years old and is essentially similar to how our own Solar System must have formed some 4.5 billion years ago. The disc is seen edge-on from our perspective and appears in professional images as thin wedges or lines protruding radially from the central star in opposite directions.
For the last couple of years I have been wondering if it was possible for amateurs to capture this special target but have never come across any such images. The main difficulty is the overwhelming glare from Beta Pictoris itself which completely drowns out the dust disc that is circling very close to the star. Images of the disc taken by the Hubble Space Telescope, and from big observatories, are usually made by physically blocking out the glare of Beta Pictoris itself within the optical path.
But recently I then found this 1993 paper 'Observation of the central part of the beta Pictoris disk with an anti-blooming CCD' (Lecavelier des Etangs, A., Perrin, G., Ferlet, R., Vidal-Madjar, A., Colas, F., et al., 1993, A&A, 274, 877)
Full article available here: http://adsabs.harvard.edu/abs/1993A%26A...274..877L

I then realised that it might not be entirely impossible to also record this object with my own equipment. I followed the technique described in the paper above, which basically consists of imaging Beta and then taking another image of a similar reference star under the same conditions. The two images are subtracted from each other to eliminate the stellar glare, and the dust disc should then hopefully reveal itself.

First I collected 55 images of Beta Pictoris at 30 seconds each. The dust disc is most prominent in IR so ideally a better result would be expected with the use of an IR pass filter. Since I only have a traditional IR/UV block filter I just imaged without any filter, to at least get as much IR light through as possible.

Next step was to capture a similar image of a reference star under the same conditions. For this purpose I used Alpha Pictoris as the paper suggested. This star is of nearly the same spectral type (A7IV compared to Beta's A6V) and is also close enough to Beta in the sky so that the slight change in telescope orientation should not affect the diffraction pattern. However, since the two stars have different magnitudes I needed to calculate how long to expose Alpha for in order to get a similar image which I could subtract from the Beta image.

The magnitude difference between the stars is 3.86(Beta) - 3.30(Alpha) = 0.56
Due to the logarithmic nature of the magnitude scale we know that a difference of 1 magnitude equals a brightness ratio of 2.512. Therefore 2.512 to the power of the numerical magnitude difference then equals the variation in brightness.
2.512^0.56 = 1.67, so it appears Alpha is 1.67 times brighter than Beta. This means that exposure for Alpha should be 1/1.67 = 0.597x that of Beta. I took the liberty of using 0.6x for simplicity's sake...
So I collected 55 images of 18 seconds (30 x 0.6) for Alpha.

Both sets of images were stacked separately in Registax and I then imported these into Photoshop, layered Alpha in 'Difference' mode on top of Beta and flattened the result. This produces a very dark image (which it should!) apart from the different background stars. But after some curves adjustment I was able to see clear signs of the actual dust disc protruding on both sides from the glare of the star. I was very happy to conclude that the position angle with regards to the background stars matched the official images exactly.
This raw Difference image looked rather horrible though, so to produce a more natural looking result I took the original stacked Beta image and then blended in the central parts from the Difference image that showed the dust disc. I decided to also keep the black spot of the central glare from the Difference image since the contrast with the protruding disc seems better this way.

And the result is, I believe, the first amateur image of another solar system: The debris disc around Beta Pictoris. I must say it feels really special to have actually captured this.

(In the image the dashed line indicates the true disc plane)