Do mini rex rabbits carry the dwarf gene?
Yes
They seem to average seven kits each pregnancy.
Don't bank on this. I joke that my rabbits put their heads together at night and ask, "how can we drive her crazy today?" Does fail to conceive, lose part (or all) of the litter, only give birth to a couple of babies which then develop problems because they grow too fast - the list of crazy-making tricks they come up with boggles the mind. Anyone who believes in the expression "breed like rabbits" has never tried it; not seriously, anyway.
A doe shouldn't be bred before she's 6 months old. Most does' litter numbers begin declining sometime after the doe gets to be 2 years old, with the doe becoming essentially sterile by the time she's 4 (if she lives that long). Fancy breeds aren't meant to crank litters out month after month; 3 to 4 litters per year is actually pushing it (heat goes hard on rabbits. Most breeders won't risk losing a doe to heatstroke, so they don't even try to breed during the summer. The short days of winter may make rabbits reluctant to breed, and even if they do, the cooler temperatures go hard on the babies. I have lost entire litters when the temps were in the 40's). If you get a doe to raise 20 babies in a year, you will be doing very well indeed.
The Mini Lop, the approximately 6 lb animal that appears on show tables, is a handsome little beast. Unfortunately, for many years, it seems like people have been calling anything with ears that don't go up a Mini Lop. Honestly, if I had a dollar for every time someone has told me "we got a Mini Lop for the kids, and it grew to be like, 12 pounds," I could probably pay my feed bill for a month. Because of this, people are a bit leery of "Mini Lops," and you should be, too. Unless you are buying from someone who keeps pedigrees and is working toward the breed standard, there is no telling what you are getting when you buy a "Mini Lop." If you do buy from a show breeder, be prepared to pay a hefty price; they are trying to pay their feed bill, too. You probably won't be able to charge anywhere near that price for the babies, if you are selling them as pets.