In reference to the patent: WO2011137930A1
The cited document is not a patent, it is a patent application. Unfortunately I'm not very skilled in determining the status of foreign patent applications so I hope another answer will be able to establish the application's status (and teach how it was determined). You can't infringe on an application since it isn't a granted patent. However, if the application does get granted, the protection goes back to the filing date. One thing to note is that the claims in an application are often far broader than what ends up in a resulting patent. I can't answer about whether BabyDoppler.com infringes since I don't have the claims of a granted patent to review.
As for whether you can make a small fetal doppler without infringing on someone's patent, it would depend on your design and what other relevant patents exist. It generally is a bad idea to rely upon random internet opinions in matters like this. A better approach to answering you question would be to consult with a patent attorney and request a freedom-to-operate opinion.
The document is a PCT application. To turn into something enforceable via the PCT process, it would have needed to enter the nation stage in one or more countries. The PatentScope link in the google patents page shows that it has no national stages and it is too late to file any. As Eric Shain said, it is a bad idea to rely on random internet information.