Is there an Android Equivalent to iMessage? I don't get mobile reception at home and would love to be able to send and receive SMS either via the phone or by computer.  I currently use Skype to send SMS but can't receive that way.  I have tried a few apps but nothing seems to work unless you're in mobile range.  My daughter has an iPhone and she can send and receive SMS with ease.  I have a Samsung Galaxy S III.

I am in Australia so I need a service that is available here. Google Voice is not available here.
Since you are in Australia, I would suggest trying t0mm13b's suggestion of Viber. You will have to "Validate" your account with Viber in a location that you have mobile data connection, according to this article, first, but then you should be able to use the service just fine on wifi.

If available, Google Voice is a good option. You will be able to send and receive SMS from it on both mobile network and wifi.

It is probably your best option as it doesn't require the other person to have a different application to be able to receive the messages. Most of them will require the person receiving the message to have the same application.

Google Voice doesn't require the other person to have a special application. It will send the messages as SMS. It will, however, require you to use the Google Voice application to send the messages.