my daughter's science project

what type of transmission you looking at? infared? or radio wave?
if radio wave find an old rc car replace the motor with led's and a resistor and that'll work easily enough.
infared.... well that one is outta my league atm.

 

my only issue with the phone pager is that you will need to pretty much keep the phone in one piece. I am sure the paging circuit is built into the phone circuit board. This doesn't make it very small or a pretty solution. But that certainly doesn't mean it won't work. Just build your circuit off the wires that would normally activate the speaker when the paging button has been pressed on the receiver. This will also probably require mains voltage source to power the phones base, transmitter. Something else to consider...

edit: I just took a look at your diagram, in there you state "12VDC is only power source", that makes a phone impractical. You also said, "no line of sight", that pretty much rules out infrared. With that receiver/transmitter being that cheap, the site dave supplied, it would easily be my choice. You could also fit that into a project box you can buy at radio shack.

 

Except that the transmitter and receiver in the link provided above are for data transmission and would require a microcontroller on either side. They would not be usable as is to do a simple on / off switch.

The RC car solution is the best bet. You should be able to get a cheap one for on the order of $10 and pulling out and using the circuit boards is easy, at least on the one I once used.

Bob