First of all, I would like to know for which exam are you asking about? If it is KEAM, then she can appear on the basis of the fact that you belong to Kerala. To be considered as Keralite, the birth certificate should show birth place in Kerala or passport showing birth place in Kerala or school leaving certificate of either parents showing study in kerala or certificate from the specified dist authorities.

In case you are asking about TS EAMCET, then she will be considered a non local only as she has just 2 years of study in Telangana.

Domicile Certificate doesn't automatically come. You have to apply for that. For that you need to belong to the place ot are a resident for many years.

Please revert back in case you have any more queries.