You may be able to find the ship name you're looking for in National Archives Record Group 85 Records of the Immigration and Naturalization Service (INS). The series "Register of War Brides with Children Admitted at San Fransisco, California, 3/4/1946 8/1/1948," for example, could be useful. You can see the catalog entry for this series here: https://catalog.archives.gov/id/2945674
If you have questions about this series, you can email the Textual Reference unit at the National Archives in Washington, D.C. at Archives1reference@nara.gov.
Additionally, you might consider contacting the National Archives of Australia. They have collection of records relating to war brides that might contain the information you're looking for. Here's a link to their website:
Best of luck with your search!
Thank you very much for your help.
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