The question to ask is — does United have an interline agreement with JetStar Asia?
According to
http://www.jetstar.com/us/en/plannin...ht-connections , no; there is a UA interline with JQ (JetStar), but not with 3K (JetStar Asia, the operator of SIN-PER).
We can double-check this with the expertflyer "interline view" for UA:
Code:
AA AB AC AF AH AI
AM AR AS AV AX AY
AZ A3 BA BD BE BI
BR BT BW CA CI CM
CO CX CZ DL EI EK
EN EQ ET EY FB FI
FJ FM FV FZ GA GF
G3 HA HO HU HX H2
IB IT JJ JL JP JQ
J2 KA KC KE KF KL
KM KQ KS KU KX LA
LG LH LO LP LR LW
LX LY MD ME MF MH
MI MK MS MU NH NU
NX NZ OA OK OM OS
OU OV OZ PG PK PR
PS PU PX PZ QF QR
RJ RO SA SK SN SQ
SU SV S2 S7 TA TG
TK TP UL UN UO UP
US UX VA VK VN VS
VW WF WM WP WY XF
XL ZH ZK 3M 4M 4Q
4U 7H 9K 9W
This is a list of IATA codes of airlines for whom United has an "interline agreement" (you can check bags at a United check-in desk and have them be tagged/loaded onto a flight operated by any one of those carriers).
So double-check whether your flight is operated by JetStar (JQ) or JetStar Asia (3K). If it's JetStar Asia, you have a problem -- you will need to re-check your bags at their counter on arrival.
The good news is that SIN immigration and customs are super efficient and I bet you could make that connection if EWR-HKG-SIN is on time. The bad news is that HKG-SIN has sporadic delays and is sometimes held to accommodate connecting pax from ORD-HKG (the same aircraft typically operates ORD-HKG-SIN). The good news is that JetStar tickets are pretty cheap and if you have travel insurance, you should be A-OK to buy a new last minute ticket to Perth in the event that you misconnect.
I believe that collecting and re-checking bags in Singapore always involves entering the country (clearing customs and walking to an airline counter airside, then re-clearing immigration and security).