She is a danger to herself financially. She is already talking about all the things she wants to buy me. Everytime we mention, we'd like to do this or that for DS its, "well when I have my money Ill pay for it!"
Socially she has no idea. She is intelligent. Just not when it comes to social or financial decisions. She doesnt understand sarcasm, tell her a joke and she thinks you are serious no matter how out there the statement is. She doesnt understand about social hints and cues. Ie, she will come over in the morning, hang around all day then if we say we have to go out she wants to come too. If you tell her your tired she offers to look after DS while I have a sleep. If you tell her you have housework to do she offers to help. She doesnt get that its a hint for her to leave. If you come straight out and say I want you to go you hate her and never want to see her again. Sure, its nice that she wants to help, but after talking to her (which is hard work in itself) for 6 or 8 hours, it becomes exhausting.
The time she is here, or with anyone else, its not limited to me. She spends the conversation talking at you not to you. She doesnt actually listen to anything you say.
Despite her visiting from 9am to 3:30pm one day a week, she wanted to make it 2 days a week. She cant understand why I dont want to spend all my spare time with her. Dont I like her?
This actually sounds a lot like my Mum. But I'm not in your situation because she has my Dad. She doesn't have depression but anxiety from an issue around 15 years ago and that changed her massively. But like you say, it's not her fault and it seems perfectly normal to her.

I just wanted to say I know where you're coming from. And if anything were to happen to my Dad I'd want to sit right down and go through a budget with Mum and make sure she wasn't going to spend up big, no matter how well-meaning it is. But if I were to sit down and tell her I want control of her financials and decisions, she'd be offended. Because what makes my choice right and not hers?

One suggestion regarding the inheritance, could you recommend that she see a financial planner? They could recommend that she spend $XX on an appropriate house, then show her investments that will earn her money in the long run. My experience with financial planners is that they're straight to the point, they can lay it out straight to her, this is what will happen if you don't look after your money, this is what will happen to your kids and grandkids if you blow it all and have nothing for them.

As for you going on the title, I think it's a good idea if it won't affect your centerlink.

Good luck