In free space, it doesn't matter. The power per incident area of a propagating wave is inversely proportional to the square of the distance from the transmitter. This is true regardless of frequency.
Certain frequencies are reflected, refracted, absorbed, and scattered differently by different materials. There is no single monotonic relationship until you get to really high energies, like gamma rays and beyond. At these really high energies (high frequencies), the waves basically just blast thru any material in their way, with higher energies passing thru material with less attenutation. Up to below Xray frequencies, there is no single answer, and it depends on the material between the transmitter and receiver.
Diffraction effects can make low fequencies (long wavelengths) appear to bend around objects, but this actually occurs at all wavelengths. The "near" layer where diffraction effects occur scales with wavelength, so it appears to us at a fixed human scale that long wavelengths go "around" objects where short wavelengths don't, but that is due to our perception scale. On the scale of the earth, commercial AM radio frequencies around 1 MHz are low enough to diffract around the curvature of the earth to some extent making over the horizon AM reception possible. Commercial FM radio, being 100x shorter wavelength, exhibits this effect much less for the same size earth, so FM radio appears to us to be mostly occluded by the horizon.
As Leon Heller said, this is not RF. However, it sure is an interesting experiment.
You have noticed that the magnetic field of the primary coil isn't strong enough to transfer energy over such a distance. Amplifying is a good idea indeed, but the question is: how much do you need to amplify?
The transistor you're using in your circuit needs a specific voltage in order to start conducting. The secondary coil probably won't give such voltage. What you can do, is use the transistor as an amplifier:
As you can see, a pull-up (R1) and a pull-down (R2) are used to give the NPN transistor the minimum voltage it needs. With this circuit, even a tiny fluctuation in Vin will affect the current through collector and emitter. Vout is Vin, but amplified (and inverted, but that's not a problem here). You can use Vout to feed a transistor as a switch, as your circuit shows.
However, this is theory. How much you have to amplify heavily depends on the distance between the coils, and you might need to amplify so much, that it isn't worth trying.
Do you have an oscilloscope? I would recommend you making a graph of the amplitude of the voltage on the secondary coil as a function of the distance between the coils. I'm guessing here, but I think this will be an exponential function. When the voltage is nice AC, you might be able to do this with a multimeter as well. Now you have some data and you can calculate the amplification you need at a specific distance. The needed amplification will dramatically increase when increasing the distance, is my guess. That makes this setup not very useful on further distances, and that's why we use RF.
To get you started in RF, I can recommend you the book Crystal Sets to Sideband by Frank W. Harris, K0IYE. Skip or scan chapter one about the history of radio. Chapter 2 is basic knowledge which I think you already have, so also scan it. Chapter 3 is some blahblah about a workspace, which I found demotivating because Harris expects you to have a lot. In chapter 4, the fun starts, with a crystal set.
Best Answer
Then you learned poorly. This is simply not correct. Different frequencies go thru different materials differently, but it is not true that lower frequencies (longer wavelengths) "travel farther" somehow.
Think of really high frequencies, like light. Here we can discern different wavelength with our bare eyes as colors. Surely you must realize that red light doesn't always "travel farther" than blue light.
What does happen is different wavelength react differently to different size objects that they can't go thru. There are three basic effects going on, reflection, absorption, and diffraction.
How much a certain material absorbs EM radiation is very material-dependent, and often not monotonic with wavelength. Think of color filters. A green filter blocks both red and blue light but lets green light thru, even though its wavelength is between red and blue.
Big things relative to the wavelength will block the radiation. However, waves also diffract along the edges of objects. This is sortof a wave bending along to follow the object. This happens only along a thin layer near the object, with the thickness of this layer proportional to the wavelength. Long waves, like 1 MHz commercial AM can bend around the edges of hills and the curvature of the earth better on a human scale than 100 MHz commercial FM, for example. This may give the impression that these longer waves "go further", but that's not what's going on.
Short wavelength don't bend around the same object as well as long wavelengths, but they can slip thru smaller holes in objects or between objects. Again, this is proportional to wavelength. A 10 m hole will easily let 3 m (100 MHz) signals thru, but mostly block 300 m (1 MHz) signals. This is probably why the shorter wavelengths work better between decks of a ship. They bounce around better and eventually make their way thru doors and the like, which longer wavelengths can't.