Summarize:

After a month or so of dating, you may want to take the relationship to the next level. This can be complicated if a child is involved and you and your partner need to be able to communicate openly about where things are headed.  Define the terms of the relationship. All relationships come with a set of expectations that develop naturally over time. After a certain point, however, you should have an open discussion about what you both expect. How serious are you about one another? Can you picture a future with this person? If so, how should you proceed? If not, is it worth it to continue dating for the time being? In terms of physical intimacy, a child can complicate things. Sex may have to occur when the child is out of the house and it may not be possible for you spend the night. Your partner might not be comfortable having you stay overnight until you've been together for awhile. You want to make sure you're respectful of your partner's wishes and boundaries. If you're in a serious relationship and your partner as a child, you should have a talk about the future. You need to know where you stand in the frame of your partner's family.  Do you see yourself ultimately ending up with your partner? Do the two of you want the same things in regards to family and career? Do you share similar values about raising children? Can any big differences between the two of you be reconciled in a healthy manner? In the event you get engaged or married, how do you factor into the child's life? Would you be a step parent? Would you be granted any legal rights in regards to custody? Would the child refer to you as "Mom" or "Dad" or keep using your first name? Meet the ex. At some point, your partner's co-parent will want to meet you. He or she will be invested in what kind of person you are as you'll be spending a lot of time with his or her child. Talk to your partner about meeting his or her ex and what the expectations are for your behavior during this meeting. In the event you marry or become engaged, you'll become a step parent to the child. You need to make sure you're ready for this kind of commitment.  Remember, needs should come before wants. Once you're a step parent, you're no longer the child's friend. You need to be able to set rules and encourage the child to their chores and homework and go to bed on time.  You and your partner will need to start creating new family traditions. Once you become a step parent, there will be a whole new family unit. To help the child feel like the three of you are a family, introduce new activities like board game nights, family dinners, and special games and events around the holiday season.  Communicate openly with your partner. It's unlikely to the two of you will always be on the same page in regards to parenting. You should keep communication open throughout the course of your relationship so that any disputes can be resolved smoothly.
Talk to your partner about taking the relationship forward. Have a serious discussion about the future. Consider becoming a step parent.