(UPDATE: This post is incorrect - see my next post)
That bright planet next to the moon right now is JUPITER. It's 400 million miles away from the sun and 300 million miles away from us... yet so stupefyingly huge out there in space that it reflects enough sunlight for many people to believe it's a bright star. Venus, on the other hand, will never appear high in the sky: because its entire orbit is inside our own (It and Mercury are closer to the sun), Venus will never stray very far from the horizon and is currently visible in the eastern pre-dawn sky.
EDIT:
I went outside to take a look and yes: Jupiter is near the Moon; Venus is high in the eastern sky; and almost directly overhead, midway between them, a small reddish dot... Mars! Three planets, one magnificent view!