This is possible but is a human health issue that you should discuss in detail with your doctor. Your newborn baby will be more likely to become colonised from you rather than from your dog.
What is MRSA and how does it affect animals?
How did my dog become colonized with MRSA?
Are some animals more MRSA prone than others?
What are the MRSA challenges for dogs with dermatitis issues?
What kinds of treatment are available for animals with MRSA?
Should I isolate my mrsa positive pet?
What can you do at home to help your MRSA infected pet?
What should I be asking my vet about MRSA
What is known about MRSA in cats?
Is it possible for dogs to be decolonized?
Is there bedding that will help a animal with an MRSA infection?
If family members and/or pets are mrsa positive will a newborn catch it?
Is clothing and other household items an MRSA problem for pets?
If my pet is MRSA positive will I catch it?
Will my MRSA positive pet contaminate my home?
What is known about MRSA in horses?
How long does MRSA stay alive on surfaces
Handwashing is effective in thwarting household MRSA - what's the best method?
Will my pet get MRSA if they eat infected bandages?
What is good infection control practice for Pet Visitor animals?
How can I choose a good vet
Where can I find scientific evidence about MRSA and staph in animals