There are various portable devices that measure lead II ECG for computation of HRV. Check out http://vivaquant.com/. They have a new device and good ECG processing.
You may want to try the empatica wristband. It's a bit pricy and does not compute the HRV automatically. But it allows you to receive RR intervals that can be easily used to compute HRV. It also portable and has a long lasting battery. Check it out at https://www.empatica.com/en-eu/research/e4/
you could consider using one of the many apps that link to a smartwatch. For example ithlete. https://www.myithlete.com/
They all require use of a heart rate monitor chest band and this might need modified for infants. There is an old but excellent review paper by Rosenstock (see below) . Alternatively simple, use intermittent rhythm strips as described by and colleagues
Nagiub M1, Alton K2, Avula V3, Hagglund
SAGE Open Med. 2014 Nov 6;2:2050312114556525. doi: 10.1177/2050312114556525. eCollection 2014.
Heart rate variability evaluation in the assessment and management of in-utero drug-exposed infants.
Heart rate variability in the neonate and infant: analytical methods, physiological and clinical observations
EG Rosenstock Y Cassuto E Zmora First published: 2 January 2007 https://doi.org/10.1111/j.1651-2227.1999.tb00158.x