The Code of Canon Law
Marriages are to be celebrated in the parish in which either of the contracting parties has a domicile or a quasi-domicile or a month's residence, or, if there is question of vagi [i.e., wanderers, vagabonds], in the parish in which they are actually residing. With the permission of the proper ordinary or the proper parish priest, marriages may be celebrated elsewhere (canon 1115).
The short of it is that if your local ordinary gives you permission, yes, you can fly away and be married. But unless there is some serious reason to do so, I urge you not to do this purely for the sake of your own convenience. Marriage is the joining not just of the couple but of two families and your families and others who care about you should not be excluded from witnessing the sacrament of your marriage without just cause. You can make your wedding as simple and low-key as you like without turning it into an elopement.