Answer:
Yes, eukaryotic plant cells have DNA. Everything that is considered 'alive' (animals, plants, fungus, bacteria, viruses etc) has some form of nucleic acid encoding their features. Most have double stranded DNA as their genetic code, but a few species (such as some types of viruses) have single-stranded DNA or RNA as their genetic code.
Remember; if it has proteins, it MUST have DNA/RNA.