Selling mum's home to buy another Topic April 2024

I am mum’s carer (not on paper) and power of enduring attorney. My daughter and I take care of her. Eventually I will move and mum will have to come with me. She and I would sell her home and buy another interstate, equivalent in value price ? We want to be together and closer to my daughter, her being youngest of the generation. I’m not the best in health. Will my mum loose her pension? Thanks in advance.