Constipation would be an unlikely result of the vaccination. It is more likely that it is the result of all the changes and stress of transition to a new home.
The first thing is to check in the hair around her anus for any dried poop, even a very small amount can cause problems. Massage any dried poop away in warm water and mild (not Dawn) dish soap. It may still take several hours before she has a bowel movement.
If you do not see any dried poop or especially if her attitude or appetite are affected please use the ForumQ&A to send me a note.