There are benefits to learning to be alone. You are in a vulnerable state right now, having had a loving partner, and grieving for the loss, while at the same time thinking about the possibility of a potential new partner. Be careful.

It would be ideal for you to be in a social group in which you can find and bond with friends first, rather than immersing yourself into the dating world.
It's a rat race, let me tell ya!, and there a lot of predators out there, just looking for someone vulnerable and kind. (I've been there, done that!)
Not to say you should be wary and cynical, but you have to take care of yourself first. If this means waiting a while as you adjust to singlehood, then maybe that is the wise thing to do. In the meantime, find good friends.