we're doing this as well. just had baby #2 and living in 900 sqft of space. we finally decided that springing for a small storage space to put things that we want to keep but don't need for now was worth the $ compared to buying a bigger space in the city.
we also reorganized our closet (using a home depot solution) to make better use of the entire space. put our low platform bed on risers and stored a lot of things underneath. replaced a low, wide dresser with a taller armoire and tall chest of drawers... as pp said, make the most of vertical space.
this being said, make sure to anchor all furniture to the walls to avoid your toddler pulling something down and getting badly hurt
