By that I mean the Gross Dorset Product… OK, just as little play on words from Gross Domestic Product.
Pointless talking about the Dorset economy if I don’t what what that it.
My first stop was the Office of National Statistics website. It does have GDP, broken down into regions and sectors, but a region is the South West and I can’t see an option for a county.
Their Local Statistics page may be useful to you.
I went to the Dorset LEP website and found they had a section that put the Dorset GVA, Gross Value Added as £17bn.
Dorset’s £17 billion GVA economy is strong and resilient. 52,000 businesses are based here, with low churn and high survival rates.
…
800,000 people live here, buoying the local economy with low unemployment and high levels of skills, qualifications and disposable income.
DORSET LEP – INVEST IN DORSET PAGE (Taken June 2020)
I also did a few more searches to compare and there was a spreadsheet of GVA broken down by local authorities. The one I downloaded went up to 2015 and when I totalled the Dorset authorities I spotted, it came to £16.7bn, so let’s go with the £17bn as per the LEP page.

That page said the next release date was March 2018 but I can’t see anything new.
My next task is to see if that can be broken down into sectors, and also to define what is the Foodie sector.