Yes definitely your domicile certificate will be valid even in 2019 as per past year trends,however I would suggest you to visit edistrict.up.nic.in if their would have been any change regarding such then you may came to know. So you don't have to worry regarding such little things.

Good luck for your counselling procedure :)

Feel free to ask if you have any further queries. 

Dear Abhiyanshu,

2014 Uttar Pradesh domicile certificate is not valid for UPSEE counselling 2019. This is because in a gap of 5 years, you could have shifted to another state and obtained domicile there. So it is always better to produce latest and up to date certificates. It takes only around a week to obtain the certificate.