If you were somewhere like Finland, showing would not only be easier, but would be expected with almost any purchase of a pure-bred female from a breeder.
HOWEVER! America isn't like Finland, which is a country that has tight breeding controls and breeders here are not out to make a quick buck. There are some serious things you should consider before starting to show your dog.
How well does she conform to the breed standard?
Showing can get expensive--can you AFFORD it?
Be aware that the reason *****es must remain unspayed in the show ring is so that the ones that do WELL can, in the future, be bred.
If you plan on breeding her on the event that she does well in the show ring, are you prepared to pay the vet costs of getting her hips and eyes checked and certified?
That said, to get started on showing, joining a club dedicated to her breed is a good start. There, you could probably meet responsible breeders who will give you good advice on shows, etc.
As for her going into heat so often, yes, it's possible. What you should look out for, however, are prolonged estrus (heat) cycles and excessive bleeding from the vagina during heat. This is one symptom of Von Willebrand's Disease
. (The site is for Italian Greyhound owners, but it's very well written and applies to all dogs.)