K.B.
My kids are 2 years, 2 months apart. My older one crawled out of his crib around 14 months, so we put a tent on it until he was 2. We needed the crib for baby #2, so we put him in a big boy bed right around 2 years old. But, the baby really didn't sleep in the crib for several weeks anyway. If they are any closer than 2 years, you'll probably need a second crib.
I don't remember having 2 in diapers as being a big deal. We did that for about a year before we started potty training the first. Boys potty train later than girls, and it is a long process. It doesn't usually happen over night. I spent a lot of time in the bathroom, and never could have done it with a newborn to take care of.
Everyone is different, this is just my experience! :)