Hello, I’m Nathan, and I’ll be assisting you today. My livelihood depends on your positive feedback, so your satisfaction is my highest priority.
Sorry to hear you’re having trouble.
Unfortunately this part is no longer readily available. This is a 2009 model printer, which was designed for a service life of only 3 years, so all parts and support for it were discontinued many years ago, as the printer would not be expected to still be operational at this point.
While it may be possible to find a handset, the cost of them due to their rarity is such that it wouldn't be worth the investment. You'd be better off buying a whole new printer at this point, as you can get a brand new all in one printer (though they don't make them with built in phones like this anymore) for about $80). The printer just isn't worth investing in the phone part because you can reasonably expect the printer to fail completely at any moment now.
If you really wished to pursue this, you can get a handset here: http://www.officeworks.com.au/shop/officeworks/p/brother-bcl-d70-additional-handset-for-mfc990cw-brbcld70
If looking for a replacement, I’d recommend any of the Epson workforce series printers. They tend to be very reliable, are easy to set up and use, have good print quality, and reasonably priced ink. Example: http://amzn.to/1F4fCYC or http://amzn.to/1NYUF1P
Note that these, like all consumer grade inkjet printers, are designed to be low cost and are essentially disposable after a few years, subsidized by the high cost of ink cartridges. If you wish to have a better quality and longer lasting printer, that comes with years worth of ink up front, consider the Epson ecotank models instead: http://amzn.to/1PpOj0C
Alternately, for a more business/commercial grade product that will be rated for a 5 year life, consider a laser printer. Lasers cost more up front also, but a toner cartridge can last for thousands of pages. A black only all in one laser is around $125: http://amzn.to/1JSHOlQ
while a color model is about twice that: http://amzn.to/1n4I7Q5
I'd recommend pairing any of the above with a panasonic cordless phone system: http://amzn.to/1RU2SWU
Best regards, ***** ***** for the news,