EMB145 First Officer experiences the failure of the landing gear to retract after takeoff. The QRH is consulted to no avail and the Dispatcher requests that the crew attempt to make it to destination and divert if it becomes necessary. It becomes necessary.

Narrative

We took off and the Captain called for gear up and I complied. The gear never retracted. The caution message appeared followed by the landing gear/lever disagree message following. We continued the normal call outs and cleaned up the airplane until we reached a safe altitude. Tower switched us over to Departure and he cleared us to 15;000. We asked to stay at 3;000 so we could take care of the issue at hand. We never declared an emergency. We then ran the appropriate QRH checklist; the Captain flew as I tried to fix. The QRH did not fix it so the Captain and I decided to transfer controls to me since he had more experience notifying who was needed to be notified. He then performed the crew brief and got a hold of the appropriate people. After we reached Dispatch; they told us to make our way to destination and we could divert to an en route alternate if need be in case fuel was an issue. We then climbed to 10;000 and made our way there. The Dispatcher's computer was down so he had to run the fuel numbers by hand which took longer than normal. The Captain and I both decided we would not be able to make it to destination and by about that time the Dispatcher gave us the new numbers and amendments to land in ZZZ for the diversion. We then made a safe landing in ZZZ and at no time were we in danger. The CRM was great. We could have climbed to a higher altitude to conserve fuel and also it would have been easier to contact everyone via radio at a higher altitude. It's easier to burn fuel than outright not having it.