Great questions! Yes, Telomerase is absolutely present in plants as it is in all eukaryotes. In fact telomeres were first discovered in corn by the famous geneticist Barbara McClintock.

I have read a couple of resent scientific papers that ask questions about what happens when plants loose telomerase in comparison to animals. It turns out that loss of telomerase in plants results in a much slower rate of developmental defects compared to animals. Scientists think this is happening because plants loose telomere length 10 times slower than animals when telomerase is not present. This means that they can not see an effect on development until 6-10 generations of plants lacking telomerase, were in mice it only takes one generation to see an effect.

Scientists hypothesize plants are better at dealing with the effects of telomerase loss because they have a more "plastic" development. This means that the genome in plants can change to better cope with the environment. Specifically, when a gene such as telomerase is damaged and no longer works, other genes can take over some of the damaged genes function.

As for the ability of perennials to get away without aging, I will have to take a guess at this one. Perennials do not grow as fast as most animals, they have lower physiological demands (i.e. they do not run or swim) and most of them go through periods of dormancy where they do almost nothing at all. So combining this with the fact that telomerase in plants is ten times better and they are more "plastic" in general, I think it is easy to imagine that if a human can live 100 years, then a plant can easily live 10 times as long (1000 years), and if it never grows as fast or use as much energy as a human it could live even longer. In fact, the longest living plant on record is called Kings holly and it is 43,000 years old! Amazing.