I believe all Jetstar's SIN-PER flights are 3K (Jetstar Asia), so the only way to get a bag onto that flight will be to claim it from your UA flight in Terminal 3 (after Singapore immigration) and check it in with Jetstar in Terminal 1. Jetstar does have a 45 minute cutoff, and they are known to be pretty strict about it.

I'm also afraid that you can't avoid Singapore immigration in this case, even with no checked baggage. SIN-PER is not in Jetstar's list of "Straight to Gate" eligible flights (http://www.jetstar.com/sg/en/plannin...n/web-check-in), so you will get a "web travel document" from online checkin. You then need to get your boarding pass in the departure hall of Terminal 1 before the 45 minute cutoff, though they might let you miss that by a few minutes without a checked bag. There are airside transfer counters, but those are not available for a UA-->3K transfer (http://www.changiairport.com/in-tran...it-information).

I agree with previous posters that you might make it (even with checked baggage) if your UA flight isn't delayed, but I would not personally try it. If you already bought the tickets, do consider travel insurance, and of course confirm in advance what it would cover in this exact situation to avoid a nasty surprise later. Walk-up fares SIN-PER are not outrageous, but you could easily end up paying >SGD 600. Also, if your Jetstar ticket is round-trip, make sure they won't cancel your return if you miss the outbound and buy a replacement.