DB for testing DAO layer

I need to test my DAO layer. I have read some topics on SO for this case, but still didn't come to answer.

I have seen some people saying that in this case I can use in-memory DB, like HSQLDB. But if I use MySQL or Postgre, shouldn't I miss same specific things (kind of specifics which is avaiable in Postgre but don't in HSQLDB)? Should I maybe create database on same RDBMS special for testing? Or there are any other solutions?

Technologies stack which I use in particular situation is String Boot + JPA, if there is any difference.