Zhena is correct, carpet is a problem that it habors dust mites and various allergens, not that people have carpet allergies. A solid floor, like wood or tile, which can be thoroughly, and easily, cleaned to remove allergens is a standard recommandation for patients with allergy problems.
Thank for that link, Zhena. While it was addressing a "portable" dance floor question, comments by tsb did answer a question of mine. The wife was interested in bamboo. I wasn't sure if there was some "rule" that a dance floor had to be oak, or whatever. tsb mentioned doing his home dance floor with bamboo, which suggest it would do fine.
And yes, this would be a DIY project. I have concrete slab subfloor, so it will be a snap-together floating floor or a glue-down type.