Interesting situation Mindy, and I think this is the third thread involvling what might be an asexual female on this forum in the past few weeks.
The last two didn't get treated to nicely, so you may be in a bumpy ride here.
I'm of the opinion that an asexual or low desire person can get married. It's like anything else though, be completely open from the beginning and tell anyone you start dating that sex is either not an option, or a very limited option. If a man knows and understands that you don't want or crave sex, or really even enjoy it very much from the sounds of it, and still wants to get married, then why shouldn't you be able to get married?
As I think you already understand, finding a man to marry who doesn't want much sex, if any, is pretty hard. But it's not impossible. On this board alone there is dozens of tales each month of women who are married to men who regularly turn down sex and could go months without it. So clearly, asexual/low desire men do exist and do prefer marriage (many of these wifes state their husbands do want to stay married, just don't want sex).
Depending on where you live, it could be difficult to find someone. Living in a small community far from a major centre might limit your option, but if you live in a major city, it could be as simple as trying an online dating service or a singles group. Just be 100% open an honest from the start. Remember, you can have 1,000 men get turned off by the fact you dislike sex, but you only need one to be ok with it to make it work.
I hope you find what you are looking for Mindy, all the best to you and kudos on knowing what you want and going for it.