It's technically not a CAQ, it's a Designation of Focused Practice in Hospital Medicine (DFPHM). Also in order to sit for this test, you need 3 years of unsupervised hospital clinical medicine + 3000 encounters in 3 years, meaning you have to practice as a hospitalist for 3 years prior to sitting for it.
Additional subspecialty certificates are available to ABFM Diplomates through other ABMS specialty boards.
www.theabfm.org
Now do you necessarily need it? No. I did inpatient medicine for 7 years in an urban setting without it. Could I sit for this test? Absolutely, but don't need to (nor want to lol).
Depending on where you are going for residency, the strength of your inpatient service should be enough to practice solo. Some programs have the FM residents run codes in the hospital, see their own patients in the ICU, do their own inpatient procedures, etc. I say do a fellowship if you feel like you need another year under your belt to get more exposure to inpatient medicine, otherwise it's not worth it.
That being said, Hospitalist fellowships in FM are only one year (as opposed to 3 year pediatric hospitalist fellowships) and to sit for this test you still need another 2-3 years of unsupervised clinic medicine, meaning you have to be attending status anyway to even take the test.
Hope this helps, and good luck with residency!