Since Illinois is not a state where gay marriage is legally allowed, I would recommend that both of you move to a more tolerant U.S. state, such as Massachusetts, Connecticut, Iowa or Vermont, all of which permit same-sex marriage. Alternately, I believe civil partnerships are allowed in the UK, which are not quite the same as same-sex marriage, but afford many of the same rights. If you plan to marry, those are your options. Consider them carefully and choose wisely.
If you don’t intend to be married (as it’s not a requirement for moving to or working in another country, in order to date someone who happens to live there), the next option to consider is the various immigration and/or work visa laws. You should contact an immigration specialist to find out what your options are, and how long either you or she can stay in your individual home countries, and to find out what the various rules and restrictions are.