It's ok to have different woods on different floors, although you might want them to be tonally compatible if they can be seen at once. You could put in red oak and have a stain used that brings you toward the cherry a bit...

If I'm reading this right, the downstairs flooring is cherry-look laminate and it is STAYING. The CARPET is being removed...which is on the stairs and is visible up against the cherry laminate...am I right?

OK...here we go. The stair treads would, in an ideal world (yah...I know), "work" with the cherry laminate. If you find a red oak and stain it one of the darker colours in the cherry floor, then go for it. This is where the money is going to come in...the stairs.

Upstairs, can be whatever you choose. It is a separate space and it is allowable to have different woods on different levels (not ideal...but still fully acceptable). The trick is the stairs. Get the stairs to "match" or "work with" the main floor. It is viewable to the "public" (ie. visitors) and therefore should offer as much flow as possible to the "main" areas of the house.

This would be my solution if I had limits on what was being down and where. Pay the money to get the treads to work with the cherry laminate and pick what you want for upstairs. As for allergies, cork is a great option. Dust mites don't like cork. The wax in the cork (suberin) is a natural pest deterrent. Just something to think about it.

@cancork THANK YOU that helps a lot!