Hi Tracey,
It really depends on which Disney Dining Plan you have purchased, if you've bought the regular plan which gives you 1 table service, 1 counter service and 1 snack credit per nights stay and you plan on having a table service dinner every night then yes you will only have counter service credits left. You can view a copy of the Dining Plan Brochure
HERE which will give you some information about the plan and will list all the participating restaurants. As you'll see there are many places to use your counter service credits for breakfast, the best ones tend to be the hotel food courts though.
What my family tends to do is to take some breakfast type bars from home with us to eat in our room, we then head to the parks and around 11.30am we have an early lunch using our counter service credits. This works well for us as we like to get to the parks as they open.
Desserts from both counter and table service can be kept for later, at a table service simply ask for your dessert to go and counter service desserts often come pre-packaged so just be sure to pick up any cutlery you may need later. We often do this with fruit cups or muffins that we then sometimes save for breakfast.
Hope that helps and you have a great trip,
Jo