If I understand the situation correctly, you should have no problems, your bicycle should fit normal baggage requirements :

See Travelling with sporting equipment
"Qatar Airways accepts any sporting equipment as checked baggage as part of the passenger's free checked baggage allowance mentioned on the ticket."

And Baggage allowance
1) Maximum dimensions :
The length + width + height should not exceed 158cm (by piece), 300cm (by weight).
--> Unless you're flying from USA of Brazil the allowance by weight should be applicable.

2) Maximum weight :
A single piece of checked-in baggage should weigh no more than 32kg (70lb).
--> Worst case you can remove a few heavy parts from the bicycle

I'm not sure wether you'll need to package it.