First of all, you are in a wonderful financial position Lenka! You are NOT late to the game at all, you are far ahead...but of course take caution with every step forward...
If I were you, I would keep as much of the 300K cash as possible in 100% offset as a cash buffer for unexpected situations - you could get married/kids/emergencies/interest rates hike/vacancies/big repairs+maintenance etc etc
If the mortgage broker says you can borrow a million, I would be looking at borrowing maximum 800K. And I think it's better to diversify by buying 2 400K properties in different regions, rather than one 800K house.
Hope the advice helps, all the best and remember LIVE BIG!