Jehovah's Witness view on a potential member marrying a non-Witness What is the official Jehovah's Witness position regarding a woman who is studying with the Witnesses and who wants to marry a worldly man (a man who is not a Jehovah's Witness)?  

We want to get married at a court house but she wants to make sure it’s ok from her elders.

Note that Are Jehovah's Witnesses allowed to marry outside the faith? is asking about members of the Jehovah's Witnesses, while this question asks about potential members.
A person who is studying while living with someone is usually encouraged to marry so that they are no longer living in sin.  If the person not studying (you in this case) is strongly opposed to the others becoming a JW both should evaluate if the relationship should continue. One cannot get baptized as a JW if they are living with a person without being legally married.

There are many Jehovah’s Witnesses who are married to non Jehovah’s Witness mates. They are encouraged to work hard at making the marriage a success. 
1 Cor 7:12-16 (NWT)


  But to the others I say, yes, I, not the Lord:i If any brother has an unbelieving wife and she is agreeable to staying with him, let him not leave her; 13  and if a woman has an unbelieving husband and he is agreeable to staying with her, let her not leave her husband. 14  For the unbelieving husband is sanctified in relation to his wife, and the unbelieving wife is sanctified in relation to the brother; otherwise, your children would be unclean, but now they are holy. 15  But if the unbelieving one chooses to depart,* let him depart; a brother or a sister is not bound under such circumstances, but God has called you to peace.j 16  For wife, how do you know whether you will save your husband?k Or, husband, how do you know whether you will save your wife?


As far as getting married in a court house that is perfectly acceptable and valid marriage.