Yes, you can now book an appointment for vaccination on the cowin.gov.in portal provided a slot is available. Earlier, the link was open only for registration. The appointments or scheduling of vaccination has been made available from May 1 onward. Make sure you look for the 18-44 category while booking an appointment.
The government says that citizens aged 18-44 years should mandatorily register themselves and schedule appointments online before vaccination. On-spot registration or walk-in facility is currently not allowed at private hospitals for the 18-44 years age group.