Here is a link to a blog about me travelling with my two yorkies to Europe:
Dog Jaunt : Reader’s report: Taking two in-cabin dogs from Canada to Sweden on Air Canada and DSB train : Traveling with a small dog
Check out her website
Dog Jaunt : Traveling with a small dog as it really helped me before my flight.
As you say, it is only 3 hours and I know that I have been annoyed with other people's children on flights so I figure it should be OK if a dog makes a little fuss. I found that the engine is so loud that small quiet whining can't really be heard - but loud barking would.
If you can reach your hand into the carrier (make sure it meets airline regulations and you have all the vaccinations required etc) from time to time to comfort your dog it should be just fine. Good luck to you!