We probe the feasibility of high-frequency radio observations of very rapid flux variations in compact active galactic nuclei (AGN). Our study assumes observations at 230 GHz with a small 6-meter class observatory, using the SNU Radio Astronomical Observatory (SRAO) as example. We find that 33 radio-bright sources are observable with signal-to-noise ratios larger than ten. We derive statistical detection limits via exhaustive Monte Carlo simulations assuming (a) periodic, and (b) episodic flaring flux variations on time-scales as small as tens of minutes. We conclude that a wide range of flux variations is observable. This makes high-frequency radio observations - even with small observatories - a powerful probe of AGN intra-day variability; especially, those observations complement observations at lower radio frequencies with larger observatories like the Korean VLBI Network (KVN).