There are rough brakets which may or not slightly change depnding on the teams on the server. If Ie in my server there are only 20 teams above Q70, to be able to make a full cup sorting the teams with the best Q after them will be admitted in the higher Q braket, disdegarding their q. Can happen that a q 55 faces the q 70, yes.
Also never be the lowest top of your bracket. A avg Q of 61 is likely to be the last in a 60-70q bracket. If you are several levels below the top leel of your server start your new season with an avg q ending in 7-8-9 (58,59). That'd move you down one bracket probaby where you'd be either same q or stronger than others.
Finally, check all the competitors. One might seem overpowered but might have had your same q at day 1 then took in several mr scout players hence skyrocket their avg Q.