If you are to buy a platform bed that has slats, they must be not too far apart from one another. They say the latex needs to breathe but I know some people just put the latex on a platform bed with one solid bottom. Maybe others will inform you better than me.
Since I needed a bed frame I bought the pine slat box from FloBeds with at first the 5" legs to keep it low to the ground but then switched to 7" legs. Dave sent me both since I was so unsure which size leg would be better. Since I chose a tall Wesley Allen Headboard to attach to the back of the bed, I decided to go with the 10" legs which worked out wonderful since my bed is stil not too tall but has room underneath it to store out of season clothes. I really like the split pine slat box although the pine smell took a few weeks to go away being that it was all natural and just put together for me with organic cotton on the sides. Dave sent me the headboard holders over night when I called him to let him know my furniture was arriving the next day. I love how easy it is to move the bed and I know that if I ever have to move, the bed frame (split slat box) would be easy to move out the door. I also love that before my 90 days were up, Dave was having a sale on free pine slat boxes that I happen to see and called him and he credited my card back for the slat box since all price decreases for the bed you chose that you see in 90 days you get if you inform FloBeds that you noticed it in their site.
I think there are a few on this site that bought platform beds from other sites to go with their latex beds and I know one person just added in a few extra slats. Maybe one of these members will post and let you know where they bought their bed frame and if they are happy with it.
You can probably put the mattress on the floor but it is difficult to get on and off the bed that way since I tried that with my old mattress before getting rid of it and just sleeping on a topper on the floor before ordering my FloBed. But my little dogs loved it when I was sleeping on the floor.
If you are having a baby sleep with you, that does sound like a safe method.