Even without other people stealing your internet bandwidth illegally or legally, 10 MBit/s is probably too slow—that is if you’re even getting the full 10 MBit/s. Due to the burst-y nature of web surfing, it is bound to disturb applications that require steady bandwidth (like online gaming). Youtube specifically can easily require 2.5+ MBit/s at higher resolutions.
If you’re using Wi-Fi in your home, that may also be a problem, especially concerning potential interference.
Note that fixed wireless broadband (something that Telstra appears to be pushing) may be unsuitable for gaming, depending on local conditions. Your current router is a DSL router, so you appear to not have wireless broadband currently.
If you can access the router’s web interface, you may be able to see the actual bandwidth you’re getting. Additionally, you can use a speed test service like fast.com (hosted by Netflix) to check the actual bandwidth. You may also want to use the DSLReports speed test because it collects metrics relevant to gamers (namely buffer bloat).