I often wonder about an engine failiuyr at low level and whether or not to apply flap as a matter of course if landing ahead.
What you need to do at such a time depends on a number of factors; each circumstance is different. Remember that during an engine failure in a single engine airplane at low level, you're not looking to extend your glide distance, necessarily. You're looking to decrease your touchdown speed and energy, and reduce your impact energy.
I've previously relayed the circumstances of an engine failure I had two years ago at low altitude (150' inside a narrow canyon) in a single engine airplane. I elected to continue my approach to the forced landing site with flaps up to achieve the best glide (I needed all of it), and just prior to touching down on the mountainside, I applied full flaps. I did so to allow surface contact with minimum energy, and also to put more material down to absorb the impact. The Dromader M18T I was flying has large flaps which hang down below the airplane, and I wanted that extra metal out there not just to slow me down in flight with drag, but to absorb energy should surface objects be struck. (Much like putting the fuselage between trees to let the wings absorb the impact energy, when going down in a heavily wooded area).
You need to consider your circumstance. Applying flaps earlier wouldn't have permitted me to clear the powerline I did, just before touchdown. It ran along a fence line that bordered the area in which I touched down. Know your airplane and what it can do. Making a configuration change close to the ground means you're not stabilized; this can be a control issue for you. It may also provided a needed stall margin. It will certainly affect your descent rate and angle, and particularly at low level once you've applied them, you're fairly committed to continuing with flaps...your options have become limited. Nothing is written in stone that says you must have a long stable approach into an emergency landing site...but you also want to make sure you can remain in control. Look at it this way; how often do you practice power off approaches to a forced landing while applying flaps at the last moment?
Not saying you shouldn't do it. I will say that you should practice doing it first until you're comfortable with it and I suggest you do it at first with an instructor.