
Don't know if it's possible with ( I presume ) a gangly puppy, she may already be too big, but when my Staffords were puppy's, I took them out in a Huggababy, which is a sling type baby carrier. With a bit of foam in the bottom to give it a bit of firmness, they were able to sit or lie down as they pleased, it made doing things like going on trains or buses much easier, and meant I could stick to the 5 minute rule, but able to be out a bit longer.
There are cheaper alternatives available now, but at the time, that was the only brand I came across.