Wheat-Free Noodle Paste?

I want to try a recipe that calls for homemade noodle paste. But I have Celiac Disease and cannot use wheat in recipes. Is there another kind of flour I could substitute for wheat flour to make a good noodle paste?

The dish I want to make is Varénèki a la polonaise, an hors-d'oeuvre in which the noodle paste is stuffed with cream cheese (two circled layers, one on top of the other) and then poached in boiling, salted water for 15-18 minutes.

Thank you for your replies.
 
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