If I take too long to complete the quest to get the Colorful Water Lily item, will the Giant Beaver (Creature) always be available to tame?
Nope, as said by Mirade in Forum, you can only reach them during "beaver breakout" mini world change:
You can only reach the beavers if a specific mini world change is active (Beaver Breakout). This happens with a certain probability at server save.
Source: Beaver Taming
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