You don't say when you did the split. From when you do the split until you have a laying queen looks like this:
Split (0 days)
Colony starts queens from four day old larvae (1st day)
Four days later the cells are capped (5th day, 8 days from when the egg was laid)
Eight days after that the queen emerges (13th day)
The queen hardens over the next few days (17th to 20th day)
Orients over the next few days (20th to maybe 23rd day)
Flies out to mate (between 21st to 29th day)
Starts to lay (between 27th to 30th day)
http://bushfarms.com/beesmath.htmA frame of eggs and open brood from another hive is cheap insurance if you are worried. But you have to give them time.