First you should confirm the issue is likely to be fixed that way.
If your speeds coming to your home are not hitting your current plan rates then paying for more is not going to improve that. (i.e. if you're getting 5Mbps and your plan is 25Mbps then moving to 50Mbps is still only going to see 5mbps coming through)
So first thing is what NBN plan are you on? 25? 50?
Also what speeds does a speed test show you are getting (google speed test)
The second thing is to rule out your in home setup being the cause. As a laptop I assume you're using wifi, which could be the bottle neck. You should connect your laptop directly to the modem via CAT5 cable (turn off wifi) and try your videos and run a speed test. See what you get.
FWIW NBN25 should be plenty for one person to stream videos.