What does " Doppler that matches the earths rotation " mean? That the frequency drifts back and forth over a 24-hour period? Does the zero-Doppler point of the curve coincide with when the star is on the meridian? How much Doppler shift is there, does it vary as a sine wave? Could it be induced by the relative motion of the receiver as it rotates with the earth? Is the signal modulated?

At that frequency you could be listening to 21 cm neutral hydrogen at 1428 MHz, Dopplered slightly by the sun's own motion through the galaxy relative to the source. Alpha Canis Minoris is in the Milky Way, only 12 degrees from the galactic equator, so there is a lot of neutral hydrogen around there, including several massive nebulae in nearby Canis Major and Monoceros.

What size reception lobe does your instrument have? Are you sure the signal is coming from a footprint that size within the vicinity of Procyon, or is it leakage from somewhere else? That close to the celestial equator, at dec = +5 degrees, you could be picking up a geostationary satellite (yes, they often transmit at frequencies reserved for astronomy). If this were the case, you would only get the signal continuously from one fixed spot, not from a moving target near Procyon.

Does the signal drop off if you move your antenna a few degrees away from that spot, does it do so asymettrically (indicating background emission from an extended source ) or quickly in any direction, (indicating a point source)?

Enquiring minds want to know.