Yes!! you are eligible to give the neet 2019. The candidate must have completed age of 17 years at the time of admission or will complete the age on or before 31st December, 2019 for 2019 admission.

According to neet information bulletin 2018 ** ( ELIGIBILITY CRITERIA ---(ii) The candidate must have completed age of 17 years at the time of admission or will complete the age on or before 31st December, 2018 i.e. the year of his/her admission to the 1st year M.B.B.S./B.D.S. Course.(https://cbseneet.nic.in/cbseneet/Welcome.aspx) ) 

You can also refer to this site for more info (https://medicine.careers360.com/articles/neet-eligibility-criteria)

All the best and start preparing for 2019 neet.

You can even confirm neet officials before filling the form .