To answer your question, no. You cannot simply have a yy child. At least 1 X chromosome is required to create a viable fetus. There are actually important functions on the X chromosome, where as they have found only a few actual genes on the Y (more or less the genes that turn on and off testosterone production during pivotal developmental times).
However, you can have a baby with just 1 X. She would have a condition known as Turner Syndrome. You can also have a baby with 3 X's, and it't not problem at all. Also, you can have a baby that is XXY, and he would have a condition known as Kleinfelter Syndrome and would have some female characteristics. You can even have a baby with XYY and some studies suggest those children are more aggressive (I don't believe that though).
The point is there MUST be at least 1 X to produce a viable fetus, bare minimum. So, YY could never happen.
I'm a Biologist (molecular genetics).