On days where you have such important data out now, it is very risky to fade these moves.
USD can continue to go down even more today (meaning EUR/USD & other Dollar pairs can continue to go up even more). Let it settle for the day, see where it wants to close.
Yes, a pullback is possible today, but it is not worth the risk. I've seen these days before, and the momentum can last till the close of the day. Because you had such an important news data today, which indicates that the Unemployment is now rising, so this would push the Fed to take action & start to cut rates in the next meeting.