This topic really hits my health button, S..
Newer "low-VOC" latex-type paints are safer that the more usual, and cheaper, standard paints. They are not entirely safe, but considerably better. There are also clay-based or milk-based paints that you can google and special-order that are non-toxic (though might be a problem for folks with dairy allergies, I suppose). But you wouldn't have them by this weekend.
Enamel paints (usually used on trim) give off serious $#!* over many hours (often days until they are competely cured), so I hope you either won't need to use them, or can keep your baby completely away from areas where they are used.
Whatever you do, please open windows and ventilate to the max.
This is such an important question. Modern life is filled with chemicals (in air, water, and food) that previous generations of children never had to deal with. Our bodies are not designed to thrive in this chemical soup. And some of us (I am one) develop chemical sensitivities when our tolerance threshhold has been overwhelmed.
You can't know when you or your child is approaching this invisible threshhold. But let me tell you, once you're sick, it changes everything. Usually for life. I never feel well, and often feel truly dreadful. Exposures to ANY chemicals – perfumed products, household cleaners, auto exhaust, the smell of plastics/rubber/fabrics, glues, office supplies, EVERYTHING – give me headaches, affect my ability to breathe or to concentrate, create horrible mood swings. I can't sleep when I've had strong exposures, so I avoid going nearly everywhere.
Living this way frequently feels like a lonely and uncomfortable hell. Asking people around me to refrain from using perfumed toiletries or not to "freshen" the air in their homes before I visit has brought me some ridicule and/or outraged, disbelieving responses (even from my own mother), so I seldom ask anymore. I mostly just stay away from anywhere people go. No parties, weddings, concerts, or other gatherings. I have had to leave movies and restaurants when someone comes in wearing perfume, even though I only attempt such madness during low-traffic hours.
I've also watched kids being evaluated for sensitivities. A couple of drops of the wrong chemical under the tongue can result in a calm child bouncing off walls, raging or weeping in just a few minutes. Sad and alarming.
You don't want to risk this for your child, believe me. The lifelong inconvenience and misery isn't worth it. A few days worth of paint fumes might not cause overload. But it could push your baby or others in your household closer to it.
Thanks for thinking about your precious child's health. I hope you will at least choose a low VOC paint. They cost a bit more, but poor health costs a lot more.