It might be easier to suggest that she got the suffix "Gittan" as a nickname whilst in Oz, from someone of Nordic ancestry, and that her birth name was simply Nóra. Perhaps she even got it as a child, when she was so young that she didn't realise it wasn't an Irish name. That would explain away any time in previous books you might have suggested it was Irish in origin.

It would also clear up this mixed ancestry issue you're trying to work in. The issue is when two people of different backgrounds come together they tend to either settle on using (and eventually bringing children up speaking) a shared second language, or alternatively, if one speaks a very popular language like English, and the other speaks it as a second language, that might be adopted.

In this case, if you have an ancestor speaking Irish, and another speaking Swedish, the likelihood is that together they would have communicated via a widely spoken local language. English, French, German, all would have been good candidates in the mid 1800s. But the liklihood that they would have settled on Irish, and hence their child would have spoken it, especially if they were emigrating, is very slim.

Of course, feel free to use it.

Or perhaps "Bríd Nóra," if you truly want to have her have a double-barreled name.