The issue here isn't your age.
Today having a baby at 38 is far from unusual and not problematic as we live longer and in this case your child would have older siblings should the worst happen.
The issue here is that from the tone of your post you don't see to be wild about the idea. Do you REALLY want another child?
Your partner might like the idea, but you come as a package with your other children. Why isn't that enough for them? (There may be a good reason here but you need to explore it).
Then there's the practicalities of your job, childcare and what might happen if you split up.
Thats a big risk.
Not to mention the risk that if you have another child, what happens if there are complications? What would be the consequences and impact on the children if the new baby was disabled for example. I do think when you have subsequent children at any age, you need to at least acknowledge this possibility. But more so when you are slightly older.
There there's the issue of the relationship you have with your partner. How long have you been with them? The fact you aren't married and are considering having a baby (and therefore likely to become more financially dependant on them at least in the short term) is an issue you need to consider.
Don't have a baby to please your partner. Have one because its what you want and you want without wholeheartedly because the situation you are complicates things and means you have far more risk and far more to consider than if you are a long term married couple having their first baby at 38.
Do think about it very seriously.
You might think YES this is for me. But its also ok for you to turn around and say I don't want to, to your partner and I stress that deciding you don't want another baby isn't selfish either (which might be the accusation you face if this is what you decide).