Since you have questioned how her faith as a Jehovah's Witness will affect your establishing a relationship with her, would it not also be fair to her to understand what it means for a Catholic to establish a relationship with a non-Catholic and for such an individual to marry outside of their faith?
"What are the requirements for marrying a non-Catholic Christian?"
"Technically, you only need permission, not a dispensation, to marry a Protestant Christian. To obtain permission to marry a non-Catholic baptized Christian, the following conditions must be fulfilled: (1) You declare that you are prepared to remove dangers of defecting from the faith; (2) you make a sincere promise to do all in your power so that all offspring are baptized and brought up in the Catholic Church; (3) the other party is to be informed at the proper time about the promises which you are to make, in such a way that it is certain that he or she is truly aware of the promise and your obligation; and (4) both parties are to be instructed about the purposes and essential properties of marriage which neither of the contracting parties is to exclude.
As for being married by a priest, you will be required to be married in the presence of your bishop or pastor ( or a priest or deacon delegated by either of them ) unless you pursue a dispensation to permit you to have a non-Catholic ceremony. This is known as a "dispensation from form" since it allows you to marry without observing the Catholic form of the marriage ceremony." - Jim Blackburn Catholic Answers.com
It seems that the Catholic religion discourages marrying out of the faith but is more accepting than the Jehovah's Witness religion. However, as a faithful Catholic there are certain 'promises' about your family that you must make to the Church, such as raising all children Catholic even though you are in a 'mixed marriage'. My advice is don't even consider it. If you are serious about your religion and she is serious about hers than if you get married you will open yourself up to heartache, family discord, unhappiness and a lifetime struggling for real intimacy. Find another Catholic to marry and move on with your life.