In theory, it should be possible to book a
DVC reservation while onboard without paying for the internet, since the onboard wifi is supposed to support connection to the Disney web sites without needing the paid connection. In practice, we have found connecting to any of the Disney sites that way was very slow, to the point of frustration. On the other hand, it is possible to purchase the internet onboard for a single day rather than the length of cruise, so that would be an option with much better connectivity. Using the paid internet, we have been able to manage DVC reservations without a problem. You could try connecting to DVC without the paid internet to see if it provides sufficient response. That way, you could decide in advance if you need to go to plan B and pay for a day of internet.
If the 11-month date happens to fall on a port day, another option might be using a cell phone connection if you have an international plan included with cell service. With AT&T, the single 24-hour day connection costs $12, less than half the
DCL internet single-day rate for the basic of the two tiers now available on those ships where DCL has switched to Starlink connections, which I believe includes the Treasure. I usually tether my tablet to my phone when using the international cell plan, but would do the same with a laptop if I carried one when traveling (which I stopped doing once I’d retired).