MDSORANGE,
Your low neutrophil count means you have moderate neutropenia, i.e., you are low on infection-fighting white cells. It's a good sign that you are asymptomatic (and didn't even know you had MDS) and overall healthy. Your counts are off the low end of the normal range, but aren't as dangerously low as some patients experience. Still, you need a doctor's advice about what to do.
It's reasonable for pet owners who are neutropenic to be concerned, since they should avoid common sources of infection and pets can be just such a source. But people facing an illness aren't going to feel comfortable/comforted/optimistic/positive/etc. if they have to banish "man's best friend" just when they need all the support they can get. What many people choose is a practical compromise, to enjoy the companionship of their dog but rely on frequent hand-washing and if possible have somebody else clean up after the dog so they don't have to.
There's a thread about pets for aplastic anemia patients
here and the situation is basically the same. Remember that you can be at risk of infection either as a
symptom of MDS or from
treatment for MDS. Even a successful treatment (drugs or transplant) can leave your counts temporarily even lower than before, and the lower they are the more you have to be careful.