Probably not. In American culture, it's been traditional to start babies off with bland foods, and then introduce new and spicy flavors a bit at a time. But there's no evidence that this strategy is necessary. Caregivers in many cultures give babies spicy foods as soon as they start eating solids, with no adverse effects.
So encourage your child to be an adventurous eater from the get-go! Add some cinnamon, ginger, or cardamom to his or her fruit. Stir a little mint into the peas and potatoes.
Just keep in mind that your baby's eating small quantities, so you'll want to be careful not to over-season. Start with just a pinch of spice in each dish and watch how your baby reacts.
You may discover that your little one shares your love of basil and your aversion to cilantro. Or you may find that he or she already has unique taste preferences.