A couple of thoughts:
1) Staying at the GF, I would expect they'd be able to help you arrange a taxi or something with a carseat the night before? That's what I would try.
2) Besides taking a rideshare/taxi, I honestly think walking/taking a boat/monorail to the MK and taking a bus to Riviera is the most direct option.
3) Alternatively, if the Epcot monorail opens again, you can take the monorail to the TTC, board the monorail to Epcot, walk through Epcot to the Skyliner. Or, from MK take a bus to Beach Club, and Skyliner to Riviera, but those are all pretty indirect options for a breakfast.
As a completely separate suggestion, something I plan to do when we have our first little one will be to splurge on a Doona carseat/stroller, since it's easy to travel with and will allow us to use any rideshare/taxi with infants in our own safe, easily transportable carseat/stroller. I assume, based on the character breakfast, that your little one is likely too old for it, but just a random thought that might be helpful for anyone looking to travel with infants.