Hello and welcome to this special forum

Haute route is indeed a beautiful trek, but since is quite popular, either go with agency or book your huts ahead (unless you backpack with all equipment). We are thinking about doing it in early spring ski-touring style. Definitely be prepared for glacier crossing (normal route), so either join group/hire a guide or have proper training and equipment.
It is not very demanding regarding altitude, and as mentioned you are never too far from civilization here. Better buy some advanced health insurance for high mountain rescue, rescue is very costly otherwise (and we all know Murphy's laws

)
Enjoy this magnificent country's beauty!