This app was mentioned in 4 comments, with an average of 2.75 upvotes
I use my Stock Market Stars android app to monitor prices throughout the day. I'm sure there are better more detailed apps but its simple and easy (no logins, no ads, no email address or facebook required and no spam) It also has price and mood alerts. Note this is a stock simulator so I use it to test various strategies without the actual risk.
So ok you are going to think im making up a story but heres what happened, I realized that we just couldnt pull off a pure maths approach to the problem, I explained to my partner why it had failed and why we were fooled but the guy was the aspergers side of our and just couldnt let go of the pure maths approach so while I was working at augmenting the whole system with some deep sentiment analysis he went behind our backs, took the whole pot of money and lost it all in a short blaze of glory in the forex markets of all things! (a private project of his he hadnt told us about) to say I was pissed was an understatement. Basically everything devolved from there and we all went our separate ways and onto other projects. We are socially friends now but I refused to work with him again after that.
As a side note a few years ago while discussing the whole project and prompted by friends who knew what happened I dug up and completed my side of the project just to prove a no maths point, its a two sided approach, one is a deep sentiment analysis server StockMarketMood and the other half (to inject and analyze the incalculable human element) is a crowd sourcing stock market simulator game StockMarketStars I then have automated trading bots which sift through all that and place real trades (not HFT) based on real data and do very nicely as it turns out.
You can try Stock Market Stars app, entirely free, no ads and no signup. The trading history of everyone is open to inspect and one of the players is up over a million from $10k.
I cant think of any Australian ASX specific stock investment simulators but I use a mobile app to play various strategies off the US market. Will all be late at night for you however.