I co-owned a pet sitting business with my Mother which she still owns and runs down in Florida for almost 4 years. Make sure it isn't a fly by night kind of deal. Any professional pet sitter is and should be bonded and insured. Make sure you give the pet sitter plenty of advance notice, if you are going away in April I believe you said, that is plenty of time.
A professional pet sitter will come to your home for an initial interview. This is normal and you want to know who is going to be in your home. You want to see how your animal reacts to them as well. They should also have a list of references on hand. They will also have you sign a contract more than likely, which is standard. I can give you a few pointers to help you along in your decision.
First off, choose someone who either has no employees or it is family owned and operated if at all possible. This is how my Mother and I run the company and we take huge pride in the fact we are animal lovers and we will always know that no funny business will be going on in your home. You take a risk with hiring employees, and being in someone elses home is something we take seriously. I have heard of some horror stories which I won't go into detail on here to scare you off, but lets just say that if you need to interview several people until you feel comfortable with one, then do it.
Don't get overly paranoid about hiring a pet sitter. For most of us, this is our fulltime job! We do it with pride because we love what we do. Pet sitters don't snoop through your house, they do their job and spend time with your animals. We can also perform several other tasks like bringing in your mail, watering your plants, rotating blinds and turning lights on and off so people won't suspect you are not home. My Mother has several clients she actually does overnights for in their homes!
A pet sitter will usually spend 30 minutes or more visiting and playing with your animal. For cats this can sometimes mean just sitting on the couch with them watching the TV and petting them, so make sure that you let the sitter know your cats routines. Leave detailed instructions written out on paper for your sitter and all the treats, litter, food, dishes etc that your cat will use during the time you are away. Even if your cat is very shy (which is common!) and the sitter won't even see him or her, it is a much better route than boarding an animal. Less stress and no chance of catching an illness.
Here is a website that can help you locate some petsitters in your area Pet Sitters International
If you have any questions please feel free to send me a PM, I am more than happy to discuss any concerns you might have if you choose to go this route for your baby.