There is certainly no specific designated time that an athlete must perform a skill before moving on to a different one. As soon as the coach believes that the initial skill is consistent with the correct technique, then they will start building on that skill. That being said, coaches may want to ensure that a skill is consistent, thus waiting a bit to move on to a new skill (perfection before progression is the name of the game), but in no way does that mean it has to be a year. Perhaps she was meaning that your daughter would not be able to compete the skill this year (as she is lv 3 so no layouts), thus having to wait until next season? That is the only thing I can think of unless it is a coach's rule.
As far as level placement, there is much more that goes into it than just tumbling skills. You can be placed on any level, in any order each season per whatever the coach decides(no rules about skipping). Having a full does not always equal lv 5 however. Much of the placement will also depend on the gym you are at. Larger gyms = more competition, which can = higher level standards to make the team. Some gyms might place girls on level 3 with a roundoff back tuck & standing BHS......other gyms may have not placed anyone on their level 3 without a specialty pass to a Roundoff BHS back tuck & triple toe to 3 BHS.
Since allstar cheerleading is a team sport, overall, stunting positions greatly affect who gets placed where. Should they be lacking flyers with lv 5 tumbling, your daughter could get pulled up to fly even without a full (if she is a strong flyer and fits the puzzle of the team). If they have a lot of flyers with the tumbling reqs, then she may not. I would be more concerned with her making sure her standing tumbling is consistent for the higher levels first (standing tuck, BHS tuck & series BHS to layout for lv 4. Jump combos to tuck & BHS series to full for lv 5) as you can hide an athlete in running tumbling much easier than standing tumbling in formations from a coaches perspective. Second, she should be thinking about working her flying skills (open gyms, flight classes, privates) as her abilities as a flyer will differ greatly between levels 3 & 5 (double downs, full ups, kick full/double baskets, etc.), which could be an opportunity or a detriment to getting moved up. Third is where I would care about the full quite frankly.
