Yes, yes a thousand times yes. Why would you want to put her thru a visit from Aunt Flo when it can be so easily avoided? Spaying and neutering prevents "accidents" that often lead to tragic circumstances. For the boys, neutering deftly dodges the bullet of testicular cancer. So many good reasons why spaying and neutering should be done.
Besides that, (from the Humane Society of the United States)
It happens everywhere.
In every community, in every state, there are homeless animals. In the U.S. as a whole, there are an estimated 6-8 million homeless animals entering animal shelters every year. About half of these animals are adopted, and tragically, the other half are euthanized. These are healthy, sweet pets who would have made great companions.
The number of homeless animals varies by state—in some states there are as many as 300,000 homeless animals euthanized in animal shelters every year. These are not the offspring of homeless "street" animals—these are the puppies and kittens of cherished family pets and even purebreds.