Googling "warmane lordaeron draenei starting zone quests" lead me here. I also did a check on the bugtracker and didn't find anything.
As a night elf druid, none of the draenei starting zone quests are available. While there is the draenei-only healing quest to be done with their racial, the rest of the quests in the 1-5 zone should be available to other alliance faction races.

