I suggest you get a travel agent to work this out for you. It will be worth the $100 or so.
You and your girlfriend will also need to carry a letter signed by by both parents outlining your travel plans and saying that you give permission for your daughter to travel alone with the other parent. Canadian customs can be especially picky about this when returning to Canada, and all customs people pay special attention when small children are travelling with one parent. This is a mechanism to prevent international abduction of children.
EDIT: Further to this - my wife and I have different last names. Our children have both last names (but not hyphenated - my last name is their last name, and my wife's list name is a middle name), but even so, my wife has had problems travelling with the children because of the name mismatch. If this is your situation (i.e. last names are different), I strongly advise that the parent travelling with the children also carry a copy of your child's long-form birth certificate that lists the mother's and father's names. i.e. you may need some proof that you are the parent. Again, this is particularly the case for young children that cannot convincingly speak for themselves (i.e. it's different if you are 4 years old, vs 14).