Is it safe to have my pet near my newborn?

Yes. Pets and kids usually get along well. It's best to supervise the two as they interact so you can intervene if necessary (even a loving friendly dog may not realize how big he is and may hurt the baby accidentally). This also assumes your pet is a cat or dog; turtles which carry salmonella or some other exotic pets might be best kept away from your newborn.
No. Pets can be unpredictable at times. Parents should constantly watch a baby if any pets are nearby. A dog or cat will likely sniff a baby to remember the baby's scent, and to find out what is going on, just out of curiosity. Other types of pets should probably stay away from babies.
Yes. Be cautious and use your best judgement. Always be present with your baby when your pet is near her. Acclimating your pet to the new family addition is always a good idea. Before your baby comes home bring an item of clothing that the baby has worn in the nursery home for your pet to get used to the infant scent.