I'd pack the props in a bag, make (or buy) some ready to eat food for them, call and find out when it would be a good time to come over. Bring the prints and if you get the feel that things are calm and the parents aren't too stressed, mention you have your props and what they think about doing some more shots. Forget about portfolio, think about them and what they'd like to see, use feedback you get from your prints gift. We were zombies the first weeks with our kids, 3am walking up and down the hall trying to remember nursery songs, 2pm sleeping on the couch, eating when ever, etc. It's exhausting. Having them come to your house or studio is a lot of work for them, much easier if you bring your stuff along, set up in a spare room or corner. Maybe you can even leave things in their guest room etc, make it easy for them.
Also, if it's their first, they are probably overprotective, thinking the baby might break any minute like a china doll. Get a feel for how they're doing and fit in.
My friends just had their baby and I'm itching to take photos, but on their time, when ever they feel rested enough. Especially for infant photography, you have to be very flexible, set aside a good amount of time, and not pout if nothing comes from it. Babies are unpredictable, parents are tired, stressed, worried, exhausted, elated, all at the same time. Mom might deal with post partum depression, who knows. Having a baby is completely life changing, more than having to adjust to a missing limb. Be gentle, fun, helpful, I'm sure you'll get some great pictures the parents will love and with some luck, enough great ones to add to your portfolio.
good luck and congrats to the parents!