The need for fertilizer depends on your potting mix. If it has nutrients added (stated on the bag), you probalby do not need to add any, but if it does not then I would use a balanced water soluble fertilizer at 1/4-1/2 recommended strength one time. Balanced meaning NPK numbers are all about the same (like 10-10-10, 10-7-14 etc), water soluble meaning the colored crystal stuff or liquid organic stuff, not granular soil fertilizer. If you have fertilizer for house plants, African violets etc, check the NPK numbers and use that if the numbers are appropriate (not like 30-10-10 or 10-40-10). Miracle Grow etc tomato formula will work fine. If the seedlings need fertilizer you will notice because growth rate stalls or stabilizes when it should be increasing.
I don't use peat pots for a few of reasons.
1) cost, I plant 2-3 times as many seedlings as I use so some never get planted and end up in the compost pile. So I use- re-use cheap 4" plastic nursery pots (7cents), plastic drink cups, paper cups, 16 or 32 oz deli containers etc.
2) root freedom. I want the roots to be unpotted, somewhat loose and in contact with the new soil when I transplant. I don't want them to have to grow through or around a layer of peat paper. If the garden soil is not damp and in close contact with the surface of the peat paper you can get dry spots and "bubbles" where the roots can't transition through.
3) water loss. peat pots wick water out of the potting soil so you have to water seedlings more and pay closer attention to them while they are under lights, and after transplant to the garden if the rim of the peat pot is above the soil line it will wick water away from the root ball.