Can my 6-year-old dog get shots safely if she's never had them?

Good questions. After your vet examines your pet and deems them healthy for vaccines, then its ok to proceed. There is no way to predict if a pet is going to have a reaction, and the fact that the pet never had vaccines before does not increase their chances of having a reaction. The best thing to do is to monitor Princess accordingly for 24 hrs after her vaccines for signs of a reaction, which include: vomiting, diarrhea and facial swelling.
A heart murmur is detected with a stethoscope used by your veterinarian in certain locations on the chest.
I am unsure of what was going on with the other pet that received vaccines. However if it took several months for the pet to perish, then this certainly was not caused by the vaccinations and likely was an unrelated underlying condition. Vaccine complications occur within 1-7 days at the most, if they are going to occur.
Therefore if my pet were unvaccinated at the age of 6, I would proceed with going forward with the necessary vaccinations based on his/her exposure, so discuss with your vet to determine which vaccines are absolutely necessary for your pet Princess. I hope this helps!