Hi,
I don't expect this circuit to oscillate.
But to stabilize the output voltage I recommend to use a ceramics capacitor at the output.
Depending on load current (waveform): 100nF ... 10uF
.... from a personal taste
.... but the datasheet says especially this is the most critical capacitance range.
--> thus you need to design it carefully.
"Oscillation" occurs when the circuit is "not stable".
Thus do a datasheet search for "oscillation", "stable", "stability" ... and so on.
The dataseet is full of important informations ... and links (to application notes..)
The device is considered to be stable without capacitor. But this does not mean that the output voltage is "clean".
To detect oscillation with a scope:
* use "AC" mode
* adjust the voltage to see some noise
* adjust the timing to microseconds
Oscillation waveform may be somewhere inbetween square wave and sine.
Ringing waveform is sine, but with decreasing amplitude.
It is considered as "stable" but at the edge to "unstable".
The faster the decay the more stable.
To check for stability you should cause some jump in the load current ... this causes some ringing excitation.
Best is a square wave current. Focus on the time when the current is released.
Klaus