The seedlings look good, but there may be a problem. When do you expect to plant outside? I would guess that in Ottawa that it is still quite some time. I know that people with shorter growing seasons start their plants indoors to get a start of the season, but I would guess that you may be a little early for your cucumbers. If the plant gets too big, it won't transplant well. From everything I've read, two or three weeks is the most that the plants should be started before transplanting. You may also have difficulty with enough light for the plant. The seedling will stretch toward the available light and will get really "leggy" and fragile if there isn't a strong source of light.
Here's a link that mentions transplanting and has more information on growing cucumbers:
As David said I think you are way too early. I may start a couple April 15 with the intention of planting them May 1 on some black plastic and covering them up with something like a milk jug or maybe plastic. I'm about 120 miles south of you.
They look great! Just be sure to rotate the seedlings so they grow straight rather than at an angle. You can always transplant into a larger container, like a SOLO cup or a 16 oz styrofoam cup when they get their first set of real leaves. Just cut some slits in the bottom and side of your peat cup and plant it in the larger size container.
do you have a lamp with a cool fluorescent bulb in it? If so I would put that thing right over top of this plant, maybe two-three inches away and see if it stops it from stretching for the time being until you can plant it outside. you may want to put it into a taller pot and cover the exposed stem. roots will grow from the stem and the you will also have more room to let it grow properly(not stretching vertically so much) with the proper light.