You will need to install a new system on the Q605, and if what you need is access to files on X.4 machine, you will need need System 7.6.1 or 8.1 on the Quadra. Tthe latter will indeed read HFS+, but the key thing is having the right Appleshare version installed on the Quadra, and the right version of Open Transport. Assuming you have these, 7.6.1 will work fine, assuming you have all the add-ons. (I do not know whether it can be done from 7.1 or 7.5, but I doubt it.)

I mount the drive on my x.4 iMac G5 regularly from Quadras running 7.6.1 and 8.1. Everything works as expected.

There are full instructions and downloads over on www.system7today.com .