Update on this:
Just tried running a few traceroutes. Can't get past my gateway at all even when pinging to several known IP addresses. The representative told me that there's nothing wrong at all since I can access Youtube (sometimes).
Great work Telstra, sure looks like everything is working as intended 
D:\Users\*redacted*>tracert 24.105.44.5
Tracing route to 24.105.44.5 over a maximum of 30 hops
1 <1 ms <1 ms <1 ms TELSTRA-GATEWAY [10.0.0.138]
2 * * * Request timed out.
3 * * * Request timed out.
4 * * * Request timed out.
5 * * * Request timed out.
6 * * * Request timed out.
7 * * * Request timed out.
8 * * * Request timed out.
9 * * * Request timed out.
10 * * * Request timed out.
11 * * * Request timed out.
12 * * * Request timed out.
13 * * * Request timed out.
14 * * * Request timed out.
15 * * * Request timed out.
16 * * * Request timed out.
17 * * * Request timed out.
18 * * * Request timed out.
19 * * * Request timed out.
20 * * * Request timed out.
21 * * * Request timed out.
22 * * * Request timed out.
23 * * * Request timed out.
24 * * * Request timed out.
25 * * * Request timed out.
26 * * * Request timed out.
27 * * * Request timed out.
28 * * * Request timed out.
29 * * * Request timed out.
30 * * * Request timed out.
Trace complete.
D:\Users\*redacted*>tracert 8.8.8.8
Tracing route to google-public-dns-a.google.com [8.8.8.8]
over a maximum of 30 hops:
1 <1 ms <1 ms <1 ms TELSTRA-GATEWAY [10.0.0.138]
2 * * * Request timed out.
3 * * * Request timed out.
4 * * * Request timed out.
5 * * * Request timed out.
6 * * * Request timed out.
7 * * * Request timed out.
8 * * * Request timed out.
9 * * * Request timed out.
10 * * * Request timed out.
11 * * * Request timed out.
12 * * * Request timed out.
13 * * * Request timed out.
14 ^C
D:\Users\*redacted*>