We have just had our first baby and have been given a My First Years Close & Secure Sleeper. Is this product safe for co-sleeping? Thanks

Red Nose recommends that the safest place for baby is in a cot that meets Australian Standards, in the same room as parents.
https://rednose.com.au/article/what-is-a-safe-sleeping-environment

The type of product that you describe, a co-sleeper, does not remove the risk to the baby of head & face becoming covered by adult bedding & pillows.

Many of these types of products do not have a firm base or have soft, padded sides.

Red Nose has a comprehensive information in relation to sharing a sleep surface with baby, which I encourage you to look at.
https://rednose.com.au/article/sharing-a-sleep-surface-with-a-baby

Some of the points in this article are:

Red Nose recommends sleeping a baby in a cot next to the parents’ bed for the first six to twelve months of life as this has been shown to lower the risk of SUDI

Sharing a sleep surface with a baby can increase the risk of SUDI.
A considerable proportion of SUDI occur on a shared sleeping surface.
Babies most at risk of SUDI when sharing a sleep surface are those less than 3 months postnatal age, babies who were born preterm or small for gestational age.
The risks are always much greater if parents smoke or are under the influence of alcohol or drugs (prescription or illegal) that cause sedation and impair their ability to respond to their baby.
There is a very high risk of infant death, including deaths attributed to fatal sleeping accidents, when a baby shares a sofa or couch with an adult during sleep
The article goes on to discuss the following:
When is sharing a sleep surface not safe.
Benefits associated with sharing a sleep surface
Red Nose supports a risk minimization approach

Red Nose states in summary:

Red Nose recommends that the safest place for a baby to sleep is in a cot next to the parents’ bed for the first six to twelve months of life as this has been shown to reduce the risk of SUDI, including SIDS and fatal sleeping accidents.

Red Nose supports a risk minimisation approach to sharing a sleep surface with your baby.
Bed-sharing and co-sleeping are associated with many benefits for babies and their families.
However, there is evidence that sharing a sleep surface with a baby can increase the risk of
SUDI and fatal sleeping accidents.