Suicide never makes sense to the survivors. It's a stupid and selfish act that leaves all the loved ones with many unanswered questions and tons of uneccesary and unwarranted guilt. It does help to realize that most people who commit such a selfish act are clinically sick and not fully capable of seeing their life situation for what it is.
Although age three is too young to think abstractly, hug her and love her and try your hardest to make her understand that Mommy didn't do this because of anything she did or didn't do. Three-year-olds think very concretely; your goal right now and in the years ahead should be to keep her from internalizing this as somehow being her (or your) fault. Or that she (or you) could have prevented it.
Help your daughter fight the "If only" thinking as she gets older. Mommy was sick. She was not in her right mind. She was not capable of making decisions because of her sickness.
Don't rule out play therapy with a qualified therapist; perhaps not now but when she's a little older. Studies have shown that children who have a parent who committed suicide are more likely to do the same, apparently because they learn that suicide becomes an "acceptable" method of escape or coping.
I hope this helps. May God be with you and your daughter in the days ahead. (((( Hugs! ))))
Actually, "now" may be good, too. But if you get her into play therapy now, don't start thinking that she couldn't possibly need it later also.
I say "play therapy" because young children don't have the language skills to express their emotions. That's why you see so many kids "acting out" their emotions (attention-seeking behavior, trouble at kindergarten, etc.).
I don't endorse any of these specifically; I just found them doing a quick Google search. And I don't agree with everything on these links, especially one that says to steer clear of discussing the moral issues with children (although age three is much too young for that). Nonetheless, perhaps this will help.
I Wish I Were In a Lonely Meadow: When A Parent Commits Suicide
Play Therapy Answer Center
Helping Son Cope with Father's Suicide
Explaining Suicide to Children
When A Parent Commits Suicide
Suicide and Relationships