Given the multiple instances in the movie in which Perry exhibited some degree of a clear desire to learn to fight tells me that he doesn't fight back, or at least stand up for himself, in situations where he theoretically could, not because he wouldn't like to, but because he's convinced he realistically cannot.
In a world where he's not only an exceptionally vulnerable animal, but also one in which everyone around him cannot be convinced that he could ever amount to anything above being a sensitive little prey piece, Perry has been given no reason to believe he's capable of anything more than minimalistic life of almost nothing but the mere pursuit of trying to stay alive each day.
But then there's a version where someone tells Perry he can be more. And, particularly, that he can learn to reliably fight back against (some) threats. And the point at which someone (in the case of the movie, it was Red) gives him that voice of faith, Perry wants to learn to do just that.
Perry wishes he could be someone stronger and more capable than a lonely little bilby. Or, at the very least, he wishes there was a way to somehow be stronger and more capable as a bilby. In, again, mostly the interest of efficiently surviving in the Outback as opposed to gaining points toward an ego or anything. (Though, learning that he can be more capable than he's been would, in fact, give him a bit of a rush of confidence of sorts in the moment, for sure.)
And clearly, he is capable of fending off a threat. Though, the most significant time we see him do so is in a rush of desperation when his newly adopted daughter is in immediate danger. I don't know that he's ever fully processed what happened then, though. I think, in a sense, you could argue that it was an act of almost blind desperation more than Perry suddenly realizing the extent of his ability to fight back against someone. (That someone even being a particularly fierce predatory animal of which at least one species naturally preys on bilbies to begin with.)
I think he doesn't think about it so much. Because why would he want to? It was one of the scariest moments of his life and he's just glad that neither himself nor Kylie got hurt (or worse) in that situation. For a bilby who faces so much stress so constantly, I think he is usually adamant about trying not to focus on things like that and just go about his day as per usual. Trying to, more or less, minimize as much stress he has to deal with as he can manage to. (Which generally tends to entail doing as little as possible in his day-to-day routine.)
I think, if it happened again, it definitely would be more likely make him reflect on it at least somewhat, though. Depending on the circumstances, of course.
But I think, from the perspective of writing his muse, ultimately, it would be fun to work with the idea of Perry encountering a situation that inspires the thought that he wants to learn to fight and there is someone in his life when that happens who takes it upon themselves to try and teach him. Not only someone who possibly knows what they're talking about in regards to fending off predators, but more importantly, someone who has become a support system of sorts for Perry and he already looks up to them as someone who he perceives as being wiser and more skilled at this whole survival thing than he is. (Not to say that he isn't a very decent survivor already, considering his particular circumstances but, well, it's probably safe to say that his self confidence is not exactly quite the boldest aspect of his character.)
It would also be a little bit ignorant of me not to acknowledge that, in a sense, Perry has done a little bit more than simply run and hide when faced with predators, we get once case where he's protecting Kylie in doing so, and one where he's protecting himself prior to meeting her.
The latter of which certainly isn't in the vein of actively fighting, but seems evident of the idea that Perry has realized, at some point in his life, that, sometimes, he can sort of work around his general lack of capability to fight back by taking advantage of the environment around him.
Which, he may or may not realize, is relatively admirable in its own right.
Perhaps working smarter, not harder, as that saying goes.