If I play Leblanc and copy an Elder Dragon, does that mean that I get all of its non-play abilities including the 1 damage is enough to kill all?

Yes, if you use a LeBlanc effect to create a copy of an Elder Dragon, your copy will have Elder Dragon's passive ability: "Any amount of your damage is enough to kill enemy units."

Here is the breakdown of how this works based on the rules:

1. What is Copied

According to the Unleashed patch notes on Copy Effects, copying a card copies all of its "copyable traits," which include its rules text (abilities). Since the passive ability is part of Elder Dragon's printed rules text, your copy inherits it.

2. What is NOT Copied (or doesn't apply)

• "When you play me" Trigger: The triggered ability ("When you play me, choose up to one enemy unit at each location...") only triggers at the specific moment the original Elder Dragon card is played from your hand. When LeBlanc creates a copy (such as a token that becomes a copy), that token is not being "played" from your hand in the way required to trigger that ability. Therefore, the "Deal 1" effect will not occur.
• The Passive: Because the passive ability is a static, ongoing effect ("Any amount of your damage..."), it functions as long as the copy is on the battlefield.

3. Summary

You will not get the "Deal 1 damage" enter-the-battlefield effect, but you will get the passive ability that makes all damage you deal to enemy units lethal.

Note: As this is a copy effect interaction, if your specific version of "LeBlanc" grants the copy "Temporary" (as seen in some copy-based mechanics), remember that the unit will be removed at the start of your Beginning phase.