Firstly, yes, your pup should have had a series of 3 vaccinations by now, but it is not to late to start, nor is it harmfull. We recommend neutering at 5 1/2 to 6 months of age so you will want to get this done promptly. For low cost care and low cost or free spay or neuter programs, contact you local Human society or SPCA, or Shelter. The first link below lists programs available by state.
http://www.lovethatcat.com/spayneuter.html#states
http://rulingcatsanddogs.com/animal-shelters-dog-cat-humane-societies- SPCA-Northern-United-States.htm



