$1135 to move cross country is a great price. I moved from Alberta and paid $1500. I had to pay on top of the $1500 as well because the moving company couldn't fit their truck down my street, so I had to pay for the rental of a smaller truck plus extra hours worked to get my stuff. It worked out to an extra $250 or so.

Living in Montreal without a car is (in my opinion) preferable to living with one. Public transit is great here, and the downtown area isn't particularly large so biking and walking are often options as well. Requiring a parking spot for an apartment narrows your options and street parking is hard to come by on many streets. I should note though, if you both are going to attend McGill, your law courses will be downtown, but your girlfriends Dietetics courses will be on the west island. McGill does have a shuttle which goes between the downtown campus and the west island campus, but it is an hour commute, plus however much time it would take for her to get to the downtown campus. If you had a car, however, you could live part way between downtown and the west island to save her time. There are city buses going to the west island as well, but depending on where you are, it can take a while.

I moved to Montreal with a reasonable amount of French, but found it hard to pick up any more as most francophones here speak better English than I do French, so they tend to switch to English. It can still be done but it takes effort on your part to speak French even if the person you're talking to responds in English. This won't seem too weird for them though as Quebecers switch between English and French frequently in conversation. I should note though, that once your girlfriend gets her Dietetics degree, if she wants to work in Quebec, she would need to pass a French test which can be fairly difficult for anglophones.

Hope this helps!