No, both are incorrect. Here are natural alternatives: 1. I'm eager to eat my dessert when I complete my task for the day. 2. I'm looking forward to eating my dessert when I finish my task for the day.

You'll need the "am:" "I am eager to eat my dessert..." "I am looking forward to eating my dessert..." And then it's better to use "after" to signal its completion (the task), and since the task will be completed in this scenario, you can leave out the "will." "...after I complete my task of the day." Also, there is an extra 's' in dessert when it refers to food rather than a climactic zone 'desert.'