get a pet door.....
or a baby gate.... the cat will be able to jump up over it or squeeze through it... and the dog, may learn to 'tell' you all when he wants to go and eat.
Our dogs have always been able to 'communicate' real well and 'talk' to tell us things.
I would, also put a 'bell' on the door... so that when it is opened or closed, you will know.
It would also be a good 'reminder' about the door. AND will serve as an 'alarm' if your baby opens that door... alerting you.
Eventually, well like right now, just for safety sake and a walking baby... you do need to get baby gates for the stairs or any dangerous door openings or doors leading outside etc.
If you still need to get rid of the cat... then an option would be to take it to an animal shelter/human society... so someone can adopt it.
I guess, I also don't understand why, if the cat is upstairs it has to eat on the kitchen counter???? But if it were the dog, there would be no problem with the dog eating upstairs???
And when we had cats... we kept the litter box in a utility room which was a bit of a distance away from everything. Meanwhile our cats (2) ate somewhere else.
Here are baby gates for stairs:
http://www.amazon.com/s/ref=nb_sb_ss_i_3_9?url=search-ali...
Good luck,
Susan