For projects that should take between two and six weeks, is Scrum the right way? Having read up on Scrum a bit, I was left with the impression Scrum is an excellent choice for mid to large sized projects.
Depends on your velocity. Usually a sprint is around 2 weeks. Using a formal process for just 3 sprints seems a bit overkill to me. I would still recommend using it, but not be so rigid about sticking to the process too much.
I think the point of scrum is that it delivers business value throughout rather than just at the end, I guess you have to decide whether your project can do that and whether it needs to do that.
Also read this, very simple explanation of how scrum works, you will be able to think about how it will affect your project while reading. http://www.softhouse.se/Uploades/Scrum%5Feng%5Fwebb.pdf
I've run short projects of around 5-6 weeks using 1 week sprints - I found it useful to have each sprint run from Wednesday->Tuesday - the team was fresher for the final two days of the sprint, and carried through the rest of the week by new stories!
One thing we struggled with in 1 week sprints was getting stories tested - we would sometimes start a new iteration with some stories not formally tested. Here we had to "tweak" the process a little to perform tests over 2 week cycles.
In short, it's doable, and you can still reap the benefits of iterative development. You just might find yourself making a few compromises in the process.
We do Scrum for short projects all the time, I find it it is much more productive for short term stuff than the waterfall approach or similar phasing.
Just one word of warning: start bugfixing from day 2, keep testing intensely. Our first Scrum tries led into truckloads of bugs to fix (for free) after the delivery of the product.
Nowadays we maintain a stringent "not done until free of bugs" policy, per story, which works wonders, without hurting productivity! If it's broken it's not in the release.
Have fun at Scrumming!