Thanks for the continued discussion! I forgot to mention we also have the poly lining under the house as well.
It sounds like having a crack with a panel heater and possibly a dehumidifier might actually be a significantly cheaper alternative. I've just got back from Noel Leeming and they've given $850 as an estimate for install of a heatpump, which is already almost twice as much as a panel heater + dehumidifier combo. This fiscally rules out getting a heatpump for just the bedroom.
@mdf yep definitely agree that I wouldn't want Bubs relying on white noise, however, I think running the dehumidifier while she's not in the room might be a good compromise. Your comment, " We went through a similar thing - old draughty damp first home, mortgage, a new born, and down to one income", perfectly describes our position. Due to my wife having ongoing issues with her mental health (bipolar depression) she hasn't been working for a couple of years, and there is no expectation for her to go back (I'd rather have a happy wife!!!). This is also why I don't want to draw any more funds from the mortgage than necessary. The panel heater + dehumidifier also means I'm not using borrowed funds to pay for it.
@Aredwood I actually came across a GZ thread where they talked about DIY maintenance on heatpumps. Managed to do a thorough clean earlier today and she seems to be running a bit better - there was quite a bit of dust build up in the filters.
Thank you again everyone!