Are there multi-day tours from Alice Springs that take infants?

Uncovery has answered your actual question, but are you sure it's the right thing to be asking?

The reason those tours are all split over multiple days is that distances around the Northern Territory are long: it's a 500-km, 6-hr drive one-way from Alice Springs, and access to Kings Canyon via the only paved road adds several hundred km to the trip. If you take a tour from Alice to Kings and Uluru and back, you'll thus be spending most of those days sitting on a bus rolling ~1500km through featureless desert, trying to keep the baby on your lap happy. As a father of two, this does not sound like my idea of a good time.

I would thus recommend skipping the package tour and flying straight from Alice to Uluru, it's a short hop and the cost is pretty reasonable. Then rent a car -- prices are again surprisingly sane given the sheer remoteness of the location -- and tour on your own, Kata Tjuta is only about an hour way. We rolled our package this way when we visited a few years ago and were very happy to be able to set our own schedules and get away from the tour groups.