I come from a divorced home. My opinion is, since you do have children, you shouldn’t just jump right away into dating.
Take into account your children’s feelings first. Discuss it with them. (How old are they?)
Even if they’re not old enough to understand, you have to explain to them -depending their age- that you will be looking into finding them a new father. Again, depending on their age, it may be hard for them to adjust to a new person taking over the responsibility as being their father. Please, when dating someone, take this into account. Make sure, you always include your kids in your decision. Yes, it is about your feelings, but don’t leave your kids out of the loop either. No one likes surprises, especially younger children who may still have attachment to their father. If they are older, they may be able to understand it easier.
Either way- if you didn’t have children, and if you are emotionally healthy to move on, then by all means, go right ahead- the longer you wait, the more doubt will arise.
Good luck in your search for a new husband/father to your kids.