No. You should split at first and then, if the relationship continues, the other person should start contributing. If you make about the same, it should be about even. If one person makes more, they often pay more. If the couple is doing something that one partner really wants to do, but the other doesn't -- the person who wants to do it should pay.
However, make sure that since guys do most of the asking, you should pick something affordable and not try to impress her with a fancy date that she didn't get to influence the location of. A third bit of information that girls sometimes try to get guys they aren't really attracted to to "grow on them," whereas guys generally date out of immediate sexual attraction. We have less incentive on early dates, sometimes. Paying a lot to hang out with someone you aren't that keen on can make you even less likely to want to get to know him. Grabbing a beer or coffee or a cheap meal are better for the first few dates.