I expect you will need to collect and recheck your bags in Jakarta, although you may be able to do that prior to clearing customs and exiting the secure area.

However, Jakarta Airport (like many airports in developing countries) has a reputation for valuables going missing whilst in transit, so I would recommend taking all your luggage with you, even if it's inconvenient. My experience is that all the non-budget hotels offer included/free airport transfers if you contact them in advance, so it shouldn't be a hassle to bring the scuba gear with you.