Definitely! But better go with a friend in case you have trouble with the steep slope and need help

There are plenty of buses to upper Bukit timah road outside hindhede drive, which is the main road leading to the park. The nearest subway station is beauty world, also walkable from there to park entrance

This is what stated at the NParks website: Keep our nature reserves a safe haven for our native biodiversity. Dogs are known to scent mark places they visit thus affecting the movement of native animals and they may also bark at or otherwise harass native animals found within the reserves. Do not bring dogs to these nature reserves and parks: Central Catchment Nature Reserve, Bukit Timah Nature Reserve, Kranji Marshes, Labrador Nature Reserve, Sungei Buloh Wetland Reserve, Upper Peirce Reservoir Park, Upper Seletar Reservoir Park, Sungei Buloh Wetlands Extension Park, Windsor Nature Park and all trails leading into the nature reserves, including trails in MacRitchie and Lower Peirce trail, the Upper Peirce Reservoir Park access road, the pipeline at Bukit Timah, the Bukit Timah Mountain Biking Trail and the Chestnut-Gangsa Biking Trail.

Free

Take the original route from Hindhede Drive (Off Upper Bukit Timah Road). Most of the walking will be on slope. The first will be the steepest. Overcome it the rest should be fine. After the first slope will be a little rest pavilion. After the second rest pavilion, will be about 80-100 steps awaiting just do it slowly keeping yo one sife. it should be fine. After the stairs it will be the summit. A pair of comfortable walking shoes and bottle of water needed. Park opens on Saturday, Sunday and local public holidays only. Park closed at 5pm. Best to start the climb at about 9am.