Right, as you surmise the construction to which you refer is zero rated anyway. However, beware; if your turnover reaches 82K in any one year you must register for VAT. Turnover is the total of all standard, reduced and zero rated supplies you make.
Your invoice for this work, as you are not registered, should make no mention of VAT (a company I operated once was not registered and to avoid confusion I always endorsed invoices to the effect that it was not registered). You should be billing for the full amount for which you are contracted, in this case 2544, and that is the amount which should have been posted to your accounts as fees received. The invoice of 2120 was, I regret to have to tell you, incorrect.
If you are not registered for VAT you should not consider it when issuing invoices. On the other hand, of course, your purchases of materials will bear VAT and you must include this as part of your cost of sales as unregistered you cannot claim it back. When you close your accounts at the year end the whole net profit, upon which you will be, in basic terms, taxed will come out in the wash as it were.
I do hope my reply has been of some assistance.