You can bake carrots and sweet potatoes and mash those very easily. Bananas are good, too. Otherwise, the OU has specific rules. Remember that kitniyot (legumes) are not allowed for Ashkenazic Jews but are OK for babies.
Per the Star-K, specific baby foods that you're allowed to feed your kid are:
Gerber 2nd Foods, 4.0z Glass Jars ONLY
- Carrots
- Squash
They also say this:
Baby food and baby cereal sold year round may not be used on Passover.
This includes rice cereal and jars of fruits and vegetables because they may
be produced on chometz equipment.
This year, a Kosher For Passover baby food is available – see page 81. [Note: that's what I copied and pasted above.]
The following are additional kitniyos options for your baby. Please note that
kitniyos is permissible for a baby (see page 55). These foods may not be
prepared or cooked on Kosher for Passover utensils.
Serve with disposables.
1. Recipe for Homemade Baby Rice Cereal:
Purchase rice (without additives, vitamins, or enrichments, and
check for extraneous matter before Pesach)
Boil 1 cup checked rice (as above) in 2 cups water & cook for 20
minutes, in separate pot used only for Kitniyos
For thicker consistency, strain or blend the cooked rice (with
separate utensils used only for Kitniyos)
Add one scoop (1 tablespoon) Kosher for Pesach vanilla sugar
Mash by hand
2. Gerber 2nd Foods Green Beans, Peas in 4 oz. jars ONLY, bearing OU
symbol, are chometz free. No Passover symbol or OUP is required.
http://www.star-k.org/kashrus/star-k11_pesach_directory.pdf (page 89 of the directory)
We bought trays for the high chair and bowls, plates, cups, and utesils that are just for Passover. If you're as strict as us, you might want to do the same (or you can cover your high chiar tray with contact paper or heavy-duty foil).