...in order for the climbing plants to have a structure to cling to. If you're somewhat handy, you could definitely do it yourself. But there are definitely companies you can hire to do this - I'd start by looking at companies that specialize in hardscapes and landscaping. If they don't build pergolas, they likely will know someone who does. That's a pretty common structure for people to have, so you should be able to find several people near you to provide pricing.

Good luck! Post some photos when it's done - I'd love to see the finished product.