The traditional gift for the first anniversary is paper. Since she likes handmade and frugal, how about a card, journal book, framed piece featuring paper crafting with an Irish theme? You can certainly get Celtic rubber stamps and if you are near a large town or city, local craft stores may have classes on rubber stamping and other paper crafts.
Or, a chain of origami figures, or one nice one affixed to a blank card. Again, a large craft store will have the papers and little books on various figures.
The modern first anniversary gift is clocks, in case that has any special significance.
Variations on the theme to get your imagination going:
Gift Suggestions to Purchase for Your 1st Anniversary:
•An anniversary journal to record your memories of your anniversaries throughout your marriage. You may think that you will never forget how you celebrated your anniversaries, but the chances are you will! Write down how you spent your anniversary together and what gifts you gave to one another.
•Road map describing a trip to take together.