The data in our relational DBMS is getting big, is it the time to move to NoSQL?
A few gigabytes is not very "big". It's more like the normal size of an enterprise DB. As long as you go over PK when joining tables it should work out really well, even in the future (as long as you don't get TB's of data a day).

Most professionals working in a big data environment consider > ~5TB as the beginning of the term big data. But even then it's not always the best way to just install the next best nosql database. You should always think about the task that you want to archive with the data (aggregate,read,search,mine,..) to find the best tools for you problem.

i.e. if you do alot of searches in you database it would probably be better to run a solr instance/cluster and denormalize your data from a DBMS like Postgres or your SQL Server from time to time and put it into solr instead of just moving the data from sql to nosql in term of persistence and performance.