I don't doubt that you intended this meaning but doesn't that seem unnecessarily ambiguous to you? Usually when people say "dozens" they mean some small handful of dozens with an absolute number probably smaller than 200 (otherwise most would say "hundreds"). Few people are going to think "hundreds of trillions" when someone says "dozens". If one is expected to think "hundreds of trillions" in this case, it seems they should be equally expected to think "hundreds of quadrillions" which would be incorrect here.

Even if one agrees that "dozens" is accurate to mean "hundreds of trillions" it still misses the mark for the argument because the odds come from the high number of planets. That is to say, there are very low odds that any individual planet harbors life but ostensibly much greater odds that one planet in a set of planets harbors life. Saying "hundreds of trillions" gets that point across better than "dozens".