Size of purebred Persian and when to spay?

Around the end of last year I purchased a purebred Persian. She is now 5 months old, but only weighs about 3 pounds. I'm wondering if I should expect her to get much bigger or not. Is it typical for Persians to be this small? Is it safe to get her spayed at this weight (vet said we could discuss when she gets her next shot)? She's been getting her shots in a larger time frame than most kittens due to her size. Vet said she doesn't feel comfortable giving such a small kitten 3 at once. I've had several other cats, but none of them have ever be this small, purebred, or Persian. She's in perfect health now and fed a raw commercial diet consisting of the honest kitchen, primal, and nature's variety instinct. She did have some rectal prolapse problems in the past, but I was able to quickly figure out that the hard food was the problem. Unlike what people expect of the breed she is extremely playful and loves to run around. There are 2 other cats living with her. The younger one is on the smaller side and the older one is average. I separate all of them when they eat. Most of the time she acts like the energizer bunny and wants to sleep, stare at people, and get pet when she's tired. After that she's up and running again, playing with cats and people. Not sure if any of this has bearing on her size or not.

Now is a good time to get her spayed.  Kitties can be spayed as small as 2 pounds.  Believe me, you don't want to go through a heat with an unspayed kitty!!  Been there, done that!  As to her size, I've had no experience with Persians, so can't advise you on that.