I think based on his interaction so far you have a case against shared custody. Not that I think that is in her best interests though. Perhaps you can ask for a schedule that increases his time with her as she gets older, both in the total amount of time, as well as the length of visits.
Has he been taking her for overnights? If he has, then I think offering him every other weekend and a visit one weeknight every week is a good start. You can write it up so that if this works well until she is say 2 years old, then he can have her for an additional night, maybe Friday night as well as Saturday and Sunday (if he can drop her off to daycare). Or you could write in that she does not have to go to daycare on one day of the week, that she spends that day with her grandparents and that night with her dad.
As she gets older you can move towards a shared custody arrangement, with the stipulation that he actually participate in her care and be a responsible dad by picking her up for visitations etc. That way, you both have time to adjust to the new situation, and he has to show responsibility to "earn" his time with her.
I really think being reasonable with a plan like this will show you are thinking about your childs best interests and acknowledging the importance of the realtionship of father and daughter. You are not denying him his time, but challenging him to show that he really wants it. I don't think the court would automatically award shared custody based on his past of scant involvement (and no CS) so this is a plan that would be acceptible in court as well.
Good luck!
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