I figured it out!
Thanks to step 4 here (https://wikibase.consulting/transferring-wikibase-data-between-wikis/), I found out I was right and that Wikibase was trying to create a Q1 where a Q1 already existed. Therefore, I just needed to move the counter to the appropriate number.
Luckily, the above link has access to a script which will do this quick and easy. You can download the link into the root directory of the Wikibase instance using:
curl https://gist.githubusercontent.com/JeroenDeDauw/c86a5ab7e2771301eb506b246f1af7a6/raw/rebuildWikibaseIdCounters.sql -o rebuildWikibaseIdCounters.sql
And execute it with:
php maintenance/sql.php rebuildWikibaseIdCounters.sql
Super fast and painless!
(The raw script is also available here if curl isn't an option for some reason: https://gist.githubusercontent.com/JeroenDeDauw/c86a5ab7e2771301eb506b246f1af7a6/raw/88cdccb1adcdf420d17a3a21296a99f153b95a21/rebuildWikibaseIdCounters.sql)
This is what the script looks like in full:
-- By Jeroen De Dauw / https://Professional.Wiki
-- License: GPL-2.0-or-later
SELECT * FROM /*_*/wb_id_counters;
REPLACE INTO /*_*/wb_id_counters VALUE((SELECT COALESCE(MAX(CAST(SUBSTRING(`page_title`, 2) AS UNSIGNED)), 0) FROM `page` WHERE `page_namespace` = 120), 'wikibase-item');
REPLACE INTO /*_*/wb_id_counters VALUE((SELECT COALESCE(MAX(CAST(SUBSTRING(`page_title`, 2) AS UNSIGNED)), 0) FROM `page` WHERE `page_namespace` = 122), 'wikibase-property');
SELECT * FROM /*_*/wb_id_counters;