My child does not imitate sounds or babbles. Should I get a hearing test done?

Yes. If your child is not developing their verbal skills at the expected age, they should absolutely have their hearing tested. Even though most infants have their hearing tested at birth, these tests are not 100%, and a normal test at birth does not eliminate the possibility of hearing loss.
Yes. Most infants will coo within the first few months and will start babbling by 6-9 months. If your infant is not babbling by 9 months or if you have any concerns that they cannot hear, you should definitely discuss with your pediatrician getting his/her hearing tested. Almost all infants have a hearing test done at the hospital at birth, but hearing loss can develop after that test.
Yes. The american academy of pediatrics recommends routinely testing hearing at birth and yearly thereafter. If this was not done, in light of current symptoms, you need to get it checked.
Yes. Glad this important question was asked. Some parents find it hard to think their baby might have a problem, especially if testing was already done and things seemed ok. Because early intervention by teams is crucial for children with disabilities, the sooner the diagnosis is made the better. I agree with dr mandelbaum. If parents suspect a problem, they should schedule an appointment and keep it.