Is that all a rubber ducky antenna is? 48" of wire wound around a
flexible core of some type?

No, that isn't all that a 'rubber duck' antenna is, wish it were
that simple. Since the question was asked, I have to assume that you
aren't exactly familiar with what a transmitter 'looks' for in an
antenna, or how that 'looked for' thing is arrived at. (And if you
aren't sort of 'involved' in radio stuff, why should you be?) Once
you learn about all that stuff it really isn't all that hard to
figure. But that 'learning' can certainly be a real chore!
- 'Doc