Does my 3-month-old daughter need a male role model in the household?
While I'm glad you're sensitive to this issue, your concerns are premature. For a child this young, the gender of the people who care for her is far less important than the fact that she's loved and protected. That's where I'd focus my efforts for the first year.
As she becomes a toddler
, however, it would be a good idea for her to have some regular interactions with an adult male she can bond with. This should be someone who's likely to have an ongoing role in her lifea relative or godfather, perhaps, not someone you're dating. This will help her feel more comfortable with men, and give her experiences that complement the ones she has at home.
When you look for a preschool and kindergarten in a few years, you may wish to find one that has at least one male teacher. (Unfortunately, this is still relatively rare.) Again, this will help your daughter get used to different social styles and ways of interacting.
But for the time being, don't worry about it.