PanKot – there are a few possible solutions.
The simplest is to talk with your downstairs neighbour about the worst areas of noise transmission into their Unit, and for you to place some rugs or some similar coverings over those areas in your Unit. Maybe hire some in the first instance to assess their effectiveness together with your neighbour; there are some companies who hire floor-coverings for special events and the like, so check those.
The least simple and possibly the most expensive is to again insulate the gap between your neighbour’s ceiling and your floor boards. There are some newer techniques available such as strategically drilling into your neighbour’s ceiling and injecting low-expansion foam which takes-up the space and fills any voids between there and the undersides of your floor.
The last solution, and one that’s certainly the most aggressive (and expensive) is to install an insulated false-ceiling below the one that exists in your neghbour’s unit.
There are a number of companies in Greater Sydney and elsewhere that specialise in floor /ceiling insulation, but as I don’t know where you’re located it’s better for you to source those yourself.
The advantage of the last two (2) options is that your neighbour would be sharing the costs, and that would focus his/her mind upon how bad the noise transmission issue really is.