I think your child is off to a great start.
Being of a chinese background, I would like mine to speak (at least some) Mandarin and Cantonese as well as Minan (the dialect of my ancestors) as well as English. Malay is also a possibility (I have family from Singapore and Malaysia), but not necessary. Being in Canada, he/she will also learn at least a little French. Depending on where my loved one comes from, perhaps her dialect as well. It won't be easy, but something worthwhile never is.
In my family, my parents spoke primarily Minan although I picked up quite a bit of Mandarin and Cantonese while I was growing up. I'm still learning Mandarin, but I would be lying if I said I was fluent (at least speaking it). I speak a smattering of a few other languages that I've picked up along the way (some Japanese, some Korean, some latin-based languages). It's not easy, but the more exposure you have to it, the easier it will be.
I will say this much though. I find a lot of Mandarin speakers have problems learning Cantonese and vice versa. Not sure why, but I do see that case often.
In-Jaul