This is not a bad idea but remember that antennas extend a couple of feet. I think they use a wire inside a hollow metal segmented shaft. The wire is wound onto a spool to retract and unwound to extend. Because the shaft is metal, the wire doesn't kink.
Do a search for "keyboard extension" or similar terms. There's a guy on here who had the same need and built one out of lego technic parts and a spare motor he had. He's got video of it working. Pretty cool.