When to let kids meet new girlfriend

Excuse me if this question has been asked before, but when is the
appropriate time to let children meet a person you are dating? My ex and I
have some disagreements about this. I feel that I should be in a
relationship long enough to know that it has the potential to be lasting
before I subject my daughter (6 years old) to meeting the person I am
dating. I don't believe that my daughter should be exposed to every person
I go out with, or her mother, just for a matter of convenience. My ex wife
has dated three different guys over the past five months, and now my ex is
with someone new again. I asked her to please give her relationships time
before having the person around my daughter, but the new guy is already
wanting to go to my daughter's T-Ball games, etc. Am I crazy for thinking
that it's unfair to my daughter to be exposed to these guys so quickly? Am
I unreasonable thinking that my ex should wait six months or whatever amount
of time it takes to see if the relationship will turn serious?