Thank your for your query.
I am not sure if your partner is holding has her passport or if it with the Home Office. If she does have her passport, you both can go to the registrar to give notice of marriage. As your partner is a non-eea national with no leave and has appealed, this does not count i would say as relevant immigration status, the registrar will automatically refer the matter to the Home Office. The Home Office will either raise no objections to the marriage or they may proceed to an interview to verify that the relationship is genuine and subsisting.
If you partner does not have her passport, you may request a certified copy of her passport from the Home Office.
I am presuming, as you have not set why your partner's EEA application was refused, that the application has been refused on the basis that you have not lived together for two years hence why you considering in getting married. Or maybe that the Home Office refused the application on the basis that it is not genuine? if this was the case, it may be difficult to get married. In any event, your partner and you have a right under Article 12 of the European Convention on Human Rights which provides for the right to marry.
Please note that this response is given to you as information only as does not constitute a legal advice as per just answer policy.
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Thank you for your query.
Sorry for the delayed response.
I would consider lodging the appeal as you have rightly stated that the regulation does not ask for two years relationship. Assuming that you get permission granted by the Tribunal and later the Tribunal finds that you are in a durable relationship, the most the Tribunal can do is refer your case back to the Home Office to make a new decision based on the Tribunal finding. The Tribunal cannot order for your partner to be given a residence card.
So if you want your partner's case resolved quickly, I would ask you to consider getting married and make a new application on the basis that your partner is married to an EEA national.