There is, however, an airside bus, as this will be an international-to-international connection.

Security from landside at T1 is pretty respectable these days, so the major limiting factor would be immigration at T3, which can be pretty horrendous, depending on the passport you hold and what's arrived before you. So if you can give some indication of timing and nationality, it'll help decide!

Of course, you can always head for immigration, see the size of the queue, and make a call as to whether you should just divert to "flight connections".