For convenience, I'm going to use "Q1" to refer to the Q played by John DeLancie.
There is, in canon, no direct answer for this. There's some evidence that points in two different directions.
There's mixed evidence in canon for this (and against it). In the Star Trek: Voyager episode Death Wish, Quinn, the Q who wants to die and later takes the name Quinn states that the Q were once like humanoid life forms. However, he never mentions any history of savagery. Since Quinn is disenchanted with the Q, it could mean that either he has a twisted view of them or a more realistic view of them then the rest of the Q.
In The Q And the Grey Q1 says or implies strongly that the Q were never created, but always have been as they are.
While this is not authoritative and Q1 is quite irascible, he seems to stick to the truth and, where possible, tell a truth that will be frustrating to the humans in the situation. He doesn't tend to lie and doesn't seem to need to.
In terms of canon, these are the only references we get to the history of the Q. (I had hoped for more from Death Wish, but there really wasn't much there in terms of Q history.)
Later, in Q2 Q1's son, referred to in the title as Q2, writes an essay on the history of the Q, but we never find out what's in it. (But the fact that there is a history implies that they've done more than just exist in the continuum for all eternity.)
Other than these examples, there's nothing in canon about the past of the Q, and with this scanty information, it's more likely Q1 is right than Quinn, who had is own view of the Q and the continuum.