Would he be okay with me converting into Judaism?

[KarinaSanchez]

I am 26 years old and dated a Jewish man for over a year. Recently he told me that he wanted to find someone who is compatible with him for a long-term relationship (that is Jewish). He never asked me to convert or indicated anything similar to that nature, however, recently I have really been considering converting. I have became familiar with the values of Judaism, and it is a lifestyle and values that I would like to follow. I have a daughter from a previous relationship, therefore, I am wondering if she would have to convert as well? she is 8 years old. And if anyone suggests that I share my feelings about converting with him? I do not want him to think that I am doing it for him, as I am not, it is something that I want to do. Last, if he wanted to pursue a relationship with me, would it have been expected for him to share his desire for me to convert unto Judaism?
He is conservative.