Certified GKH Gardening Expert
I didn't find much about rupturewort, except that it is considered weedy and didn't fare too well in a groundcover test. The ASPCA has a good list of toxic and non toxic plants and it isn't listed there either. I did find it in a UK publication that said it was toxic.
Here are some other options. If you find one you like, look it up on the ASPCA website: https://www.aspca.org/pet-care/animal-poison-control/toxic-and-non-toxic-plants
https://www.gardeningknowhow.com/lawn-care/lawn-substitutes/lagen/lawn-alternatives-warm-areas.htm
https://www.gardeningknowhow.com/lawn-care/lawn-substitutes/lagen/plant-alternatives-to-traditional-lawn-grass.htm
https://www.gardeningknowhow.com/lawn-care/lawn-substitutes/lagen/high-traffic-lawn-options.htm