To add to other answers - you can also get a taxi between the two terminals BUT the taxi drivers on the 'taxi rank' may be unwilling to make the short lowish-price (not low) trip between terminals as they lose their place in the queue. So standing at the main entrance and acquiring a taxi from an arriving passenger is probably easiest.
Overall, Sydney airports (both ends) are very accustomed to transferring people between terminals and you should have no problem getting there promptly.
However, as you are probably aware, the normal check-in time for an international flight is 3 hours, you usually have no problems at 2 hours preflight and somewhere after that things start getting marginal. You are in the marginal zone, as you know. In your position I would check to find out how Gregs advice " ... Upon arriving in Sydney, make your way to the transfer lounge at Gate 46 and check in for your international flight. ..." applies to your flights. ie is "Gate 46" a universal transfer gate - if so all is well, or if not, what is the equivalent gate for your flight - it is almost certain that this arrangement applies for all airlines flying internationally out of Sydney.
As you are single ticketed with UNITED, that seems the logical place to start asking.