Hi Bardy,
Moving house (even 500m) is a fairly substantial change. So much so that you could be on a completely different exchange and cable path to your previous location.
Pings are low priority traffic and do not paint the whole picture. This is explained in further detail here: http://crowdsupport.telstra.com.au/t5/General-Internet-KB/International-routing-latency-and-ping/ta-p/309783
Also, with a change of premises, there may be new variables impacting the WiFi signal in your home in a way that it didn't previously. This next link provides some basic checks that you can perform: http://crowdsupport.telstra.com.au/t5/General-Internet-KB/WiFi-Troubleshooting/ta-p/107516
In all circumstances, speed issues can depend on a number of factors depending on the technology type, the configuration of the equipment, the capabilities of the network and the demand on the network and the internal wiring of your home. This next link provides a few other checks that you may find helpful: http://crowdsupport.telstra.com.au/t5/Home-Broadband-KB/Speed-Issues/ta-p/278139
If you continue to be concerned about the speeds after reading and performing the tests in the above links, please contact Tech Support on 133 933 if you have not already done so. They will be able to access your account and arrange for this to be tested further and/or for a technician to attend.
- Shelly