Hi
@shaycamp21 ~ So excited for you! My mother is from Singapore and we have many friends and family there. My family and I have been fortunate to travel extensively throughout Asia and you're going to have a wonderful time. I am pretty certain that your cruise will stop in Penang, Malaysia, which is where my father is from, as it's a very popular (and usually everyone's favorite port) and a wonderful city island.
We have done the
travel agent route, especially when there's a need for a visa and a time crunch. Otherwise, we typically book flights on our own. I would confirm visa requirements. Travel agents are helpful if you don't want the stress of booking, but otherwise their main expertise is helping with visas, if needed. If you don't need visas (or can easily apply online for one), then I don't really see the need to pay for a TA. I'm also a Type A person, though, and I like to control my own itinerary and choose my own seats, etc. As such, using a TA is not always conducive to my personality, as I hate having to go through a middle man for something that I can do online by myself. Obviously, if you're not a Type A person, then this characteristic would not apply to you!
I use Google Flights. Perhaps there's a better search engine, but I like Google Flights. It's far too early for you to book international flights right now - as your trip is 11 months out - but getting a good idea of options as of right now, it looks like Air Canada, ANA, Korean Air (through Seoul), Cathay (through Hong Kong), and Singapore Airlines have the most frequencies/options. Singapore Airlines (SIA) is my favorite airline in the world. It is by far the BEST option and if you're OK with spending a little bit more, you will be highly rewarded. Even the experience in the economy cabin is superb to any other airline I've ever flown. Commitment to safety, quality, etc. is incredible. SIA "retires" their aircraft after ~10 years, and sells the aircraft to other airlines, thus keeping the youngest fleet in the industry. I was surprised there wasn't a non-stop option between Toronto and Singapore, but it looks like you're going to have to go from Toronto to Vancouver and then non stop to Singapore.
For the most part, Asian airlines are far superior to North American carriers. We flew Korean Air from DC to Seoul on one leg of our honeymoon and it was a wonderful experience. I've also flown ANA and thought the service and food was great. The aircraft (from DC) was a little older, but it was no different - and certainly younger - than United Airlines and Air Canada's aircraft. I've heard wonderful things about Eva and Cathay from family + friends, but have never flown them personally.
I highly recommend, as someone in the hospitality industry (hotels), booking directly through the airline's website. For instance, if you use Google Flights and see a route that you'd like to book with Singapore Airlines, I would then go to
https://www.singaporeair.com/ and book the route directly from Singapore Airlines.
Regarding getting around Asia, there are smaller "regional" airlines, you can find most information online. I would recommend not flying Philippines Airlines. Cousins just flew them from Manila to LA a few days ago and mentioned that the Manila Airport was not good (too small and very tedious, inefficient security process that would be an issue if you had a connecting flight). Malaysia Airlines, despite its high profile crashes, is very safe and a top airline in the area. There are "budget" airlines in Southeast Asia (just Google them). I've flown Air Asia, Tiger, and Scoot and found them to be no different than short flights (1-3 hours) on American Airlines, United Airlines, etc. and certainly a better experience than America's Frontier Airlines and Spirit!
Sorry for the long response - let me know if you have any follow up questions. Always happy to help and I can direct message as well. Have fun planning and I hope you have the most wonderful trip! Singapore and Japan are incredible countries and will really appreciate your tourism dollars right now!