BA are great for travelling with babies, they allow a buggy and a carseat in addition to your baggage allowance as well as a baggage allowance for your baby in addition to your own.
Having travelled using both a bugaboo and maclaren, I would personally recommend using a maclaren or pushchair as they are easier for travelling than the bulkier bugaboo if you have that option. The maclaren folds down easily at the gate, easily folded down and stored on trains and take up less space in your hire car (have many a time put it accross the back seat floor to free up the boot space) As for carseat on bugaboo wheels, if you are planning on doing sightseeing or there being times where your bub spends a great amount of time in the buggy then I dont think they would be as comfortable in carseat on the wheels, in my opinion. As for carseats, if you do decide to take your own I would check the regulations in Canada and make sure your carseat is allowed. Likely will be fine but there are differing laws across the globe (e.g. Australia doesnt allow the use of isofix carseats) so you dont want to take your carseat over to find you cant use it.
Honestly in our experience the less you have to carry with you the easier it is so you might want to think about once you are not using a hire car how often will you need the seat because you will have to carry it with you for the rest of the 2 weeks as well as your luggage, baby stuff (nappy bag etc), your bub etc... That pretty much goes for everything, less is just easier.
Hope you guys have a great time, it is a great age to go away with.