Can I run 125kHz RF circuit on a breadboard?
In my experience, yes, but you may need to take a few things into account.


Some breadboards are better than others. The maximum frequency I've seen operating cleanly and reliably on a breadboard is 2 MHz. I've also seen breadboards that couldn't handle 200 kHz.
You need to consider the maximum frequency present on the breadboard, not the largest "fundamental" frequency. For instance, a square wave signal (such as a clock or the 555's output) have very large harmonics up to maybe 5 or 7 times their fundamental frequency. If the breadboard can't handle these, then the clock will become distorted (low-pass filtered); additionally, if those harmonics spread through the breadboard, they'll distort potentially all your signals.
Bypass capacitors become important as the frequency increases. Put one cap everwhere a circuit connects to the supply or ground, and you may have to sprinkle them around wherever high-frequency harmonics appear.