Yes, fix this with a unique index on the FK field. The reason why you need to fix it now is that you can't control how badly people are going to insert data over time when the database is not set up correctly with controls that do not allow the behavior you do not want.
The first time you havea a duplicated record inserted into the child table, you might break a lot of code. With no unique index, the chances of a second record getting inserted can be quite high. You can say, you'll control this at the application level but that is usaully a poor choice as there is no guaranteee that other applications, bulk inserts etc aren't gong to happen that circumvent the application. Putting things right as soon as you can in a database design is critical. It becomes really hard to fix a poor design when there are a lot of records in the database.