You have the right idea, but it's not quite the same as 'Let's get moving'. 'Let's' is a suggestion. You would say this to another person before you leave, in order to encourage them to move. You might say 'Away we go' or more commonly 'Off we go' AS you are starting to move. It's a kind of acknowledgement of the fact that the journey is starting.

When you go 'away' from something, you leave that something behind. 'Away we go' is a saying that generally means 'away we go on an adventure' or 'away we go on a journey'. As a movie title, I would think of that movie being about a person or a group of people leaving something behind (like their home town of their family) to go on an adventure somewhere else.

you might have misheard this phrase, the actual phrase is, "go away" which means, to leave,or to disappear.

Hello Jin, Away we go is similar to 'off we go' or, as you say, similar to lets start Hope this helps Bob