I'm guessing from this that yoyu're pretty young? Most employers don't necessarily expect a fairly young person, still living at home with Mom & Dad, to have extensive work experience.
While it never hurts to have a work history, I don't really think this will keep you from getting a job in nursing, assuming you do well in school.
Volunteering would be nice, especially if you take it as seriously as a paid job so that it can be the source of some good recommendations.
Also, think of ways to present your babysitting experience as having value outside of the $$ earned- what did you learn from that experience that would make you a valuable employee?
If I were doing the hiring, I would not expect a new graduate to have the skills of an experienced nurse. What I would look for would be evidence of a potential good employee. I would look for evidence that you were dependable and conscientious, able to get along well with other people, be a team player, willing to admit that you don't know everything yet but are willing to learn, etc etc.
If you have the opportunity to work as a nurse tech or aide or whatever during the summer, that might not be a bad idea, either.
But, again, I'd be looking for good employee material, not necessarily the most skilled person (but of course would expect the skills to come along with time).